The Design and Fabrication of an
Electrically Activated Photonic Crystal Microcavity
Laser
Alejandro Grifte
B.S.E.E., Electrical Engineering and Computer Science
Minor, Physics
University of New Mexico, 2004
Submitted to the
Department of Electrical Engineering and Computer Science
in partial fulfillment of the requirements for the degree of
Master of Science in Electrical Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2007
0 2007 Massachusetts Institute of Technology
All rights reserved.
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Author........
...............................................
Alejandro Griie
Department of Electrical Engineering and Computer Science
February 9, 2007
V/
Certified by...........
....................................
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Accepted by...............
61 U
Leslie A. Kolodziejski
Professor of Electrical Engineering
Ahesis Supervisor
......................
Arthur C. Smith
Chair, Department Committee of Graduate Students
Department of Electrical Engineering and Computer Science
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The Design and Fabrication of an
Electrically-Activated Photonic Crystal Microcavity
Laser
By
Alejandro Grifie
Submitted to the Department of Electrical Engineering and Computer Science
on February 9, 2007, in partial fulfillment of the
requirements for the degree of
Master of Science in Electrical Engineering
Abstract
Spontaneous emission can be controlled by altering the environment that a medium
radiates into; specifically, by reducing the dimensions of a cavity, excited atoms
immersed in the cavity are more likely to spontaneously emit photons into the dominant
cavity mode than spurious modes. Microcavity lasers exploit this stronger coupling by
confining photons to a cavity with outer dimensions approximately the size of an optical
wavelength. Owing to the strong coupling to the lasing mode, microcavity lasers are
distinguished for their high efficiency, low threshold, high speed, and low noise
operation. However, microcavity lasers by nature have low output power. Thus,
microcavity lasers are ideal light sources for applications requiring low power such as
integrated optics or quantum computation.
This thesis describes the design and fabrication of a microcavity laser utilizing multiple
photonic crystal mirrors. The laser is well suited for integrated optics for many reasons. It
is electrically activated and emits light in-plane. The laser conserves chip real-estate and
couples directly into an output waveguide. The one dimensional photonic crystal mirrors
prevent coupling into radiation modes increasing the quality factor (Q) of the cavity. Rate
equation analysis is used to show that the laser will have a small threshold current. A new
hybrid fabrication scheme is employed that simplifies the device processing. The step and
repeat mask design makes it simple to fabricate and to test many devices each with
varying dimensions, allowing one to empirically determine the optimal device.
Finally, a new microcavity laser capable of confining light in three dimensions is
proposed.
Thesis Supervisor: Leslie A. Kolodziejski
Title: Professor of Electrical Engineering
3
4
Acknowledgements
I am truly blessed to have such an outstanding family. Antonette, my wife, and
Angelina, my daughter put their entire lives behind them, so I could fulfill a dream. Their
sacrifice is something I will never forget. We came to Boston for an adventure, and at
times we found ourselves in the middle of a nightmare, but each trial just brought us
closer. I now feel that with each others love, no ordeal is insurmountable. I dedicate this
thesis to these two amazing, beautiful women. Andres the next one is for you my friend.
I cannot thank Professor Leslie Kolodziej ski enough for first, accepting me into
her outstanding group, and second, presenting me with the most intriguing device I could
have ever asked for. Upon dealing with Professor Kolodziejski, I can now conclude that
she is the equivalent of an optical gain medium, because all who come across her emerge
a better person (I apologize for the laser analogy). I am very greatful for both the
technical guidance and mentoring that I have received from Leslie during my time as her
student.
I also benefited greatly from the technical insights of Dr. Gale Petrich.
Throughout my time here he answered all of my many, many questions without ever
rolling his eyes (well maybe once!). Everything in this thesis, from mask design to
fabrication sequence has a touch of Gale's outstanding ingenuity. I have truly enjoyed our
many discussions.
Everyone in the Integrated Photonic Materials and Devices group has been a
pleasure to work with. Ryan Williams gave a lot of his time to show me around the clean
room and never hesitated to show me any new tricks. Orit Shamir maintained an
optimistic attitude even during the days we never left the clean room. She also saved
many of my wafers from destruction. My office mate, Reginald Bryant was a model for
hard work. It was amazing to witness Reggie's work ethic and genius during our final
class-project. I also enjoyed the company of Ta-Ming Shih who always managed to be
laid back yet diligent at the same time. This work has spawned from brilliant past
members including Solomon Assefa, Alexei Erchak, Eric Mattson, and Ed Lim. I hope I
have added a little more pavement to the road.
I would also like to thank my friend, Shahrooz Amin for his sense of humor and
never-ending enthusiasm for science. I hope some of it has rubbed off on me. I cannot
remember a time I didn't laugh during our regular coffee breaks. Joel Yang was also an
outstanding friend. Our regular discussions about family, weekends, and spontaneous
emission were always enjoyable.
The atmosphere at MIT is something I will always miss. Even with so much
pressure around, everyone was kind and helpful. I thank Jim Daly for selflessly showing
me different tools and evaporating metal on all my wafers. Rajeev Ram patiently
answered a barrage of my questions after every class.
This work would not have been possible without the support of Sandia National
Labs. I owe Armando Sanchez big time for giving my resume to Mitch McCrory, and I
owe Mitch McCrory for passing it on to Mike Daily. Finally, I owe Mike Daily for
presenting me with this opportunity. I should also thank Dr. Ting, "Willie" Luk for
5
or
exposing me to the Bragg Onion Resonator, and Dr. Darwin Serkland for suggesting the
use of ITO in my laser design.
My family in Albuquerque has supported me every step of the way. In many
ways, this thesis is the result of sacrifices made long ago by my mother and father,
Frances and Alfredo Grifne. Waking up every morning, cooking me home made breakfast
and then driving me across town to school are just some of the tasks they performed to
get me here. My wife's family, Pauline, Rick, and Maggie have contributed in many
ways to this thesis. Thank you for not making me pay you back for everything, or else I
would be in real trouble.
Finally, I am lucky to have some of the greatest friends in the world whose
intelligence and humanitarianism I admire greatly. Ben, Ismail, Ryan, Jon, Mando; bros
for life!
6
Table of Contents
Chapter 1.
1.1.
1.2.
1.3.
Chapter 2.
2.1.
2.2.
2.3.
2.4.
2.4.1.
2.4.2.
2.5.
Chapter 3.
3.1.
3.2.
3.2.1.
3.3.
3.4.
3.4.1.
3.4.2.
Chapter 4.
4.1.
4.2.
4.2.1.
Introduction..............................................................................................
12
12
M otivation..................................................................................................
13
Photonic Crystals ......................................................................................
14
Overview .....................................................................................................
Laser Basics................................................................................................
16
Background................................................................................................
16
Sem iconductor Lasers................................................................................
16
Diode Lasers .............................................................................................
18
The role of spontaneous emission in m icrocavity lasers ........................... 20
M otivation for the Optical M icrocavity................................................
21
The quantum-mechanical view of spontaneous emission: Vacuum fields 22
Other Photonic Crystal Lasers ..................................................................
27
Design and Sim ulations ...........................................................................
31
31
Design Concept.........................................................................................
34
Layered Structure Design .........................................................................
Optical Simulations................................................................................
39
41
Rate Equation Calculations.......................................................................
M ask Design .............................................................................................
46
49
Stripe Laser Diagnostic.........................................................................
Integrated Diagnostic Detector .............................................................
51
52
Fabrication ...............................................................................................
52
Fabrication Sequence ................................................................................
Fabrication Results.....................................................................................
55
Steps 1-2: Formation of ohmic contacts on p-type arsenide-based material
. . 55
..............................................................................................................
4.2.2.
Steps 3-4: W et-etching of Arsenide based material............................... 59
61
4.2.3.
Problem s with M etal Adhesion..............................................................
4.2.4.
Steps 4-5: Formation of ohmic contacts to n-type phosphide-based
m aterial ...................................................................................................................
66
4.3.
Rem aining Fabrication Steps: Discussion ................................................
66
4.3.1.
Steps 7-10: Dry etch of InP and GaAs materials. Patterning of Si0 2 hard
m a sk
...................................................................................................................
67
4.3.2.
Steps 11-12: Electron-beam lithography or Focused Ion Beam etching for
68
photonic crystal active region ................................................................................
4.3.3.
Steps 13-14: Undercut rem oval of Phosphide-based material......................
..............................................................................................................
. . 69
4.3.4.
Step 15: Etching of Si0 2 to open up contact vias ..................................
70
70
4.3.5.
Step 16: Thermal oxidation of AlAs....................................................
70
4.4.
Fabrication of a generic ridge laser............................................................
76
Chapter 5. Conclusion and Future Research ...........................................................
76
5.1.
Further Investigations ...............................................................................
76
equations.........................................................
Improvement to the rate
5.1.1.
7
Testing of the Photonic Crystal Microcavity Laser ...............................
5.1.2.
A laser incorporating adiabatic tapers...................................................
5.1.3.
A microcavity laser with mirror confinement in three directions..........
5.1.4.
Final C onclusions.......................................................................................
5.2.
Appendix 1: Index of refraction for AlxGaAs Ix ............................... .......................... . .
Appendix 2: The Phenomenological Rate equations..................................................
B ib liograp h y ..........................................................................................
77
78
78
81
83
84
92
8
Table of Figures:
17
FIGURE 1: LIGHT-MATTER INTERACTION PROCESSES.................................................................................
FIGURE 2: A SIMPLIFIED BAND DIAGRAM OF THE ACTIVE REGION DUE TO PUMPING. SHADED CIRCLES
REPRESENT FILLED STATES OR ELECTRONS, WHILE WHITE CIRCLES ARE EMPTY STATES, OR HOLES.
CO N CEPTS TA KEN FRO M [6].................................................................................................................
18
FIGURE 3 A SIMPLE EDGE EMITTING DIODE LASER WITH MIRRORS ON THE SIDE .........................................
19
FIGURE 4: EMISSION INTENSITY DISTRIBUTION OF AN X-ORIENTED DIPOLE IN A) FREE SPACE, B) A/2 ONE
DIMENSIONAL CAVITY WITH FREQUENCY CORRESPONDING TO CUT-OFF, AND C) A/2 ONE DIMENSIONAL
CAVITY BELOW CUT-OFF. FIGURES AND CONCEPTS FROM [9]...........................................................
20
FIGURE 5: PHOTOLUMINESCENCE SPECTRUM OF FABRY PEROT CAVITIES OF DIFFERENT AXIAL LENGTHS. THE
LIGHT IS DETECTED FROM THE CAVITY AXIS. AS THE DIMENSIONS OF THE CAVITY DECREASES, LIGHT IS
22
MORE LIKELY TO BE EMITTED INTO THE LASING MODE. FIGURE IS TAKEN FROM [9]. .......................
28
FIGURE 6: TOP VIEW OF A SINGLE DEFECT PHOTONIC CRYSTAL LASER. .....................................................
29
FIGURE 7: ELECTRICALLY ACTIVATED PHOTONIC CRYSTAL LASER DEMONSTRATED IN [26]. ....................
FIGURE 8: COUPLED CAVITY PHOTONIC CRYSTAL LASER [28].................................................................
30
FIGURE 9: SCHEMATIC AND OUTPUT CHARACTERISTICS OF THE LASER DESCRIBED IN [27]. THE SOFT
THRESHOLD IS SHOWN IN THE INSET OF THE L-I CURVE. ...................................................................
30
FIGURE 10: SCHEMATIC OF THE PHOTONIC CRYSTAL MICROCAVITY LASER AND GENERIC EPILAYERS. ........ 32
FIGURE 11. SCHEMATICS OF THE GROW N SAMPLES ......................................................................................
37
FIGURE 12: PHOTOLUMINESCENCE DATA FOR GROWN STRUCTURES .........................................................
39
FIGURE 13: GROWN STRUCTURES AND THEIR TRANSVERSE FUNDAMENTAL MODE DISTRIBUTIONS.............. 41
FIGURE 14: L-1 CURVES FOR THE PHOTONIC CRYSTAL MICROCAVITY LASER.............................................
45
FIGURE 15: MASK VIEWS WITH VARYING ZOOM LEVELS. THE RED OVALS INDICATE THE REGION SHOWN IN
THE FOLLOWING ZOOM LEVEL. A.) THE ENTIRE STEP AND REPEAT MASK INCLUDES 36 IDENTICAL DIES,
B.) EACH DIE CONSISTS OF 234 LASERS OF VARYING DIMENSIONS AND MANY DIAGNOSTICS. C.) EACH
UNIT CELL ON THE DIE CONTAINS 12 LASERS AND ACCOMPANYING CONTACTS. D) AN ARRAY OF 6
LASERS EACH SEPARATED BY 30ptM. E.)EACH LASER REQUIRES 8 MASKS TO FABRICATE.................... 49
FIGURE 16: SCHEMATIC OF A SINGLE STRIPE LASER DIAGNOSTIC. ..............................................................
50
FIGURE 17: MASK LAYOUT OF STRIPE LASER WITH INTEGRATED PASSIVE SECTION....................................
50
51
FIGURE 18: THE INTEGRATED DIAGNOSTIC DETECTOR ...............................................................................
FIGURE 19: FABRICATION SEQUENCE FOR THE ELECTRICALLY ACTIVATED MICROCAVITY LASER AND
DIAGNOSTIC STRIPE LASER. STEPS 8-10 WITH A DOTTED LINE AROUND THEM ARE ONLY REQUIRED TO
FABRICATE DIAGNOSTIC STRIPE LASERS BEFORE E-BEAM LITHOGRAPHY, OR IF ONE USES FOCUSED ION
B EA M LIT H O G R A PHY . ..........................................................................................................................
55
FIGURE 20: A) THE BAND DIAGRAM AND POTENTIAL BARRIER ASSOCIATED WITH THERMIONIC EMISSION. B)
THE BAND DIAGRAM AND POTENTIAL BARRIER ASSOCIATED WITH CARRIER TUNNELING. ................ 56
FIGURE 21: METAL FEATURES AFTER STEPS 1-2. A.) A UNIT CELL CONTAINING 6 ACTIVE REGIONS. B.)
ALIGNMENT MARKS C.) VERNIER ALIGNMENT MARKS AS VIEWED WITH A 50X OBJECTIVE. EACH LINE
IS 1.5[tM WIDE WITH A MINIMUM SPACING OF 1.5ptM BETWEEN EACH LINE.......................................
59
FIGURE 22: PHOTONIC CRYSTAL LASER FEATURES AFTER REMOVING THE P-TYPE MATERIAL. A.) THE ACTIVE
AREA OF A LASER WITH THE PATTERNED P-TYPE BEAM DEFINED. B.) A UNIT CELL DEPICTING A TOTAL
61
O F 12 AC T IV E A REA S............................................................................................................................
FIGURE 23: EXAMPLES OF METAL ADHESION PROBLEMS AFTER WET-ETCH. A.) ROWS OF STRIPE LASERS WITH
AN INTEGRATED LOSS-SECTION. METAL IS ONLY ATTACHED TO THE LARGE CONTACTS WHICH WERE
PROTECTED BY PHOTORESIST. B.) VERNIER ALIGNMENT MARKS HAVE MISSING PIECES WHICH
APPEARED TO HAVE PEELED OFF FROM THE UNDERLYING GAAS MATERIAL. C.) THREE ROWS OF STRIPE
62
LASERS WITH THE 3 RD ROW COMPLETELY MISSING. ..........................................................................
FIGURE 24: ANNEALED METAL CONTACT THAT WAS USED TO FABRICATE THE SELF-ALIGNED RIDGE
WAVEGUIDE. THE LACK OF SURFACE MORPHOLOGY IS PROBABLY DUE TO THE ANNEAL. ALSO, THE
SURFACE ROUGHNESS OF THE RIDGE LEADS TO AN UNACCEPTABLE RIDGE WAVEGUIDE................... 63
FIGURE 25: CROSS-SECTIONAL VIEW OF AN ALTERNATIVE METHOD TO FORM THE RIDGE OF THE STRIPE
LASER WITHOUT USING METAL AS A WET-ETCH MASK. THIS METHOD DOES NOT REQUIRE ANY DRYETCHING, BUT DOES REQUIRE GOOD ALIGNMENT DURING THE RE-PATTERNING OF MASK 1. IT IS
IMPORTANT TO REALIZE THAT ONE MUST APPLY AND PATTERN MASK 2 BEFORE WET-ETCHING THE
GAAS-BASED MATERIAL IN ORDER TO FORM THE P-TYPE BEAM OF THE PHOTONIC CRYSTAL LASERS.. 64
9
FIGURE 26: ELECTRON-BEAM FIELD ALIGNMENT MARKS INCLUDED IN THE MASK DESIGN THAT WERE
FORMED DURING SECOND M ETAL DEPOSITION. ....................................................................................
FIGURE 27: UNIT CELL AFTER STEPS 4-5. COMPARE TO FIGURE 15(C). .....................................................
FIGURE 28: ELECTRON-BEAM LITHOGRAPHY PROCESS LEADING UP TO THE ETCHING OF THE SUBMICRON
FEACTURES. SOME LAYER COLORS ARE MADE PARTIALLY TRANSPARENT TO REFLECT ACTUAL
65
66
-. 6 9
V IS IB IL IT Y ..................................................................................................................................-----.71
FIGURE 29: THE RIDGE LASER WITH ACCOMPANYING FABRICATION SEQUENCE...........................................
PL.....................................................73
FIGURE 30: GROWN RIDGE LASERS AND ACOMMPANYING
FIGURE 31: SAMPLE VA36 BEFORE THE SECOND CONTACT DEPOSITION. STRIPES WIDTHS ARE AS SMALL AS
1 .5 [pM ..................................................................................................................................................
FIGURE
FIGURE
FIGURE
FIGURE
32: L-I CURVES FOR A RIDGE LASER..............................................................................................
33: BOUNDARY CONDITIONS FOR AN OPTICAL CAVITY. ...................................................................
34: ToP VIEW OF A PHOTONIC CRYSTAL LASER UTILIZING ADIABATIC TAPERS ............................
35: 2 VARIATIONS OF A 3D MIRROR CONFINED MICROCAVITY LASER ...........................................
74
75
77
78
80
10
11
Chapter 1.
Introduction
1.1.
Motivation
Silicon microelectronics has had an undeniable impact on our society. Large scale
integration technologies have enabled the creation of low cost, high performance
computer chips that are present wherever electronic data resides. However, silicon
electronics is approaching fundamental performance limits. Many of the problems
associated with silicon electronics originate from the metal wires used for interconnects
[1]. In particular, wires are inherently resistive and as their cross sections shrink, their
resistance increases. Associated with resistive losses is heat which can adversely affect
the performance of other devices on the integrated circuit (IC). Also, as dimensions
shrink and modulation speeds increase, the metal wires must be treated as transmission
lines. Inherent to transmission lines is capacitance per unit length which affects the speed
that information can be transmitted. As the distance between wires decrease, the wires
can act like miniature antennas sending and receiving unwanted data, a process known as
cross-talk.
By transmitting information optically many of the problems associated with metal
wires can be avoided. Simple impedance arguments show that optical photons can
transmit information with less energy than electrons [2]. Optical fibers are already the
primary data path in long distance telecommunication systems. In wavelength division
12
multiplexing (WDM), many optical signals of different wavelengths are transmitted
through a single fiber. This parallelism can not be achieved with electrons which are
charged carriers. Thus, the goal of integrated optics is to extend optics' success in longhaul telecommunications, to short-range communication systems such as microprocessors
where integrated optics can act as a data link between components on a single chip, or a
communication link between chips. However, the exact architecture for implementing
photonic integrated circuits (PIC) has not been determined. In order to compete with
silicon electronics, PIC's must be small and fast while consuming little power. These
PIC's will require a light source such as a laser. The laser must also be compact, efficient,
and be able to run at high speeds.
A microcavity laser satisfies all of these constraints by its nature. By confining
light to wavelength scales, microcavity lasers are superior to large lasers in almost every
way with the exception of output power. This thesis focuses on the fabrication and design
of a microcavity laser that is well suited for integrated optics. The laser is specifically
designed to be electrically activated and emit light in-plane. A smaller optical cavity
means that light reflects off the cavity walls more frequently necessitating high
reflectivity mirrors to avoid excessive loss. Since perfect reflectors do not naturally exist
in the optical regime, lithography-defined reflectors called photonic crystals are utilized
in the design of the microcavity laser.
1.2. Photonic Crystals
A photonic crystal (PC) is a periodic arrangement of dielectric material [3]. A
unique property of photonic crystals is that they exhibit a photonic bandgap, a range of
13
frequencies in which light can not propagate within the photonic crystal.
Photonic
crystals fabricated from semiconductor material are particularly desirable, because the PC
can be fabricated using standard microelectronic fabrication techniques, and can thus be
incorporated with other optical components on a single chip. Photonic crystals fabricated
using such techniques are usually limited to one-dimensional and two-dimensional
arrangements of rods or holes on a semiconductor substrate.
The planar nature of
conventional microelectronic fabrication techniques makes it difficult to create structures
exhibiting a photonic band-gap in three dimensions, although researchers are finding new
ways to create three-dimensional photonic crystals [4].
To create a photonic crystal laser, two criteria must be met. First a resonator must
be created and secondly, the laser must have sufficient gain to overcome the losses
associated with the resonator'. A defect can be incorporated into a photonic crystal by
increasing or decreasing the size of a particular rod or hole, or by eliminating one of the
rods or holes all together. The use of a defect breaks the symmetry of the optical lattice
and creates areas or sites where once forbidden modes can propagate or oscillate
depending on the situation.
Hence, the defect within the photonic crystal acts as a
resonator. In a well designed oscillator, the resonant frequency of a mode associated with
a defect lies within the range of forbidden frequencies, the photonic band gap (PBG), of
the surrounding photonic crystal. By including an optical gain medium within the defect,
one can exploit the high reflectivity of the surrounding photonic crystal and the small
modal volume to create a very efficient laser with photonic crystal mirrors [5].
1 For microcavity lasers the gain can actually be much smaller than the loss and one can still observe
lasing. This phenomenon will be explained later in the thesis.
14
1.3 Overview
By utilizing a defect with two one-dimensional photonic crystal mirrors to trap
light in a cavity with dimensions on the scale of a wavelength, a microcavity laser can be
created. The small size of the laser conserves space and leads to a low threshold power.
The laser will be designed using simulation software, and will be fabricated using
standard semiconductor lithographic and pattern transfer techniques. Simple ridge lasers
will be fabricated to test the quality of the starting epitaxy material.
This thesis discusses the various aspects of creating a microcavity, electricallyactivated photonic crystal laser. Chapter 2 presents the basics of lasers with emphasis on
the use of microcavities.
microcavity laser.
Chapter 3 discusses the design and the simulations of the
The initial fabrication results are shown in Chapter 4.
Finally,
Chapter 5 summarizes the thesis and presents future avenues for investigation.
15
Chapter 2.
Laser Basics
2.1.
Background
The control afforded by microelectronic fabrication techniques allows the creation
of one and two dimensional photonic crystals that are composed of semiconductor
materials as well as the creation of semiconductor optical and electrical devices.
Semiconductor lasers are particularly desirable because they are relatively small, and can
be integrated with other optical components such as modulators and detectors on a single
chip. This section provides a brief background of semiconductor laser technology, and
explains the subtleties of spontaneous emission, a key process in microcavities.
2.2. Semiconductor Lasers
In general, a laser requires an emitting medium and optical feedback. A material
with an indirect bandgap, such as silicon can not efficiently emit light while conserving
momentum, so various direct bandgap III-V materials are used for semiconductor lasers.
The most common Ill-V semiconductors include various alloys of indium, gallium,
aluminum, arsenic, phosphor and nitrogen. A medium can emit light through either
spontaneous or stimulated emission, and it can absorb light through stimulated absorption
as shown schematically in Figure 1. In stimulated emission, a photon causes an electron
16
and hole to recombine and emit a second photon. The emitted photon is in-phase with the
original photon, so that two identical photons result. Conventional lasers rely on photon
creation by stimulated emission for a coherent source of light. Conventional lasers are
defined in this thesis as lasers whose optical cavity dimensions are larger than the
emission wavelength. Optical feedback is necessary so that a generated photon can return
to the emitting medium in order to generate more photons through stimulated emission.
Optical feedback is usually achieved by placing mirrors, such as photonic crystals,
around the emitting medium, so that light is confined within the cavity.
Stimulated absorption
Stimulated Emission
after
before
after
before
SDontaneous Emission
after
before
EC
EC
EC
EC
EC
EC
E
E
E
E
EV
E
Figure 1: Light-matter interaction processes.
To achieve lasing, the rate of photon emission into the lasing mode must exceed
the rate of stimulated absorption. Therefore, in a semiconductor laser, the number of
available electrons in the conduction band must be in excess of a threshold value so that
the probability of emission is larger than the probability of absorption. This is
accomplished by means of pumping the semiconductor laser from an external source.
Pumping excites electrons into the conduction band from the valence band leaving behind
holes in the empty states. Since electrons and holes both obey Fermi-Dirac statistics,
excited electrons will occupy the lowest energy states in the conduction band, while holes
will occupy the highest energy states in the valence band. Pumping leads to a band
17
diagram in the active area as shown in Figure 2 whereby the average energy required for
absorption is larger than the average energy released in emission [6]. The electron and
hole energies are characterized by their quasi Fermi levels, Efe and Ef respectively. The
quasi Fermi level is the energy at which the carrier occupation probability is 0.5. When
Efe-E;> h v where h v is the energy of the photon that is being emitted, the probability of
emission is larger than the probability of absorption, so that the material exerts a net gain
and is said to be population inverted [7].
EEmission
Absorption
E
Figure 2: A simplified band diagram of the active region due to pumping. Shaded circles represent filled
states or electrons, while white circles are empty states, or holes. Concepts taken from [6].
2.3. Diode Lasers
The simplest form of a semiconductor laser is a p-n diode with mirrors on either
end as shown in Figure 3. A p-n junction diode is used because it is the simplest known
semiconductor device in which large concentrations of electrons and holes reside in close
proximity to each other at the same time, so that recombination and thus emission of
radiation is likely to occur.
18
Optical Cavity
Figure 3: A simple edge emitting diode laser with mirrors on the side
Almost all modem diode lasers are based on separate confinement heterostructure
quantum well designs. The quantum well is formed by surrounding a small bandgap
active material with a barrier material that has a larger bandgap. The quantum well
confines electrons and holes to a small volume preventing their diffusion across the p-n
junction and hence increases the possibility of radiative recombination. Quantum wells
also reduce the volume of the gain region meaning that fewer net carriers need to be
present to achieve a given carrier density. This reduces the threshold current and also
reduces the laser's turn on time by increasing the differential gain. However, a low
volume gain region has its shortcomings. Physically, a smaller active medium volume
means less of the electromagnetic mode overlaps the gain region decreasing the effective
gain per unit length. To counteract this reduction in modal gain, lower index cladding
regions are placed on either side of the active material to separately confine the
electromagnetic mode to the gain region [8]. The cladding regions also ensure that the
optical cavity is large enough to contain an electromagnetic mode of the desired
wavelength.
19
2.4. The role of spontaneous emission in microcavity lasers
Many of the outstanding properties of microcavity lasers, such as high efficiency,
small threshold current and high bandwidth, result from the nature of spontaneous
emission in a wavelength-sized cavity. In particular, the spontaneous emission rate, the
lasing mode coupling, and the emission pattern, can all be modified by including a
medium in an optical microcavity. Figure 4 shows how the emission intensity distribution
of an x-oriented dipole is affected by a cavity [9]. The cavity is created by placing perfect
mirrors at x = ±L/2. When the frequency of the dipole, w, is such that the wavevector, k,
equals w/c=u/L=k,, the cavity is tuned to the emission frequency of the dipole and one
observes an enhanced emission intensity distribution as shown in Figure 4(b). Thus, the
usual description of spontaneous emission characteristics, being an intrinsic property of a
particular medium, is no longer accurate, because the atom and the field become a
coupled system and can not be considered separately. The study of this coupling, known
as cavity quantum electrodynamics (QED), can be complex. Therefore, the purpose of the
following sections is to give a qualitative physical description of cavity QED and its
application to microcavity lasers.
-20
() k =0.96 kc 1.04 kc
(b)k=k
(a) FREE SPACE
a)
Free space, b) V2 one dimensional
in
dipole
x-oriented
of
an
Figure 4: Emission intensity distribution
cavity with frequency corresponding to cut-off, and c) X/2 one dimensional cavity below cut-off. Figures
and concepts from [9].
20
2.4.1. Motivation for the Optical Microcavity
In conventional lasers where most, if not all, of the optical cavity dimensions are
much larger than the emission wavelength, spontaneous emission is primarily an energy
loss process. In conventional lasers, the large dimensions result in many possible
electromagnetic modes. Thus, spontaneously-emitted photons are unlikely to occupy the
lasing mode 2 . For this conventional case, spontaneous emission consumes carriers
without emitting photons into the lasing mode, the mode that experiences the largest net
optical gain, and wastes pump energy. Since spontaneous emission is usually the largest
carrier loss process below threshold, by increasing the proportion of photons
spontaneously emitted into the lasing mode, the laser is more energetically efficient.
In microcavity lasers, the optical cavity dimensions are on the order of an optical
wavelength resulting in much fewer possible optical modes, and thus a higher probability
of coupling into the lasing mode assuming proper cavity tuning as shown in Figure 5. The
coupling probability is quantified in the spontaneous emission factor,
3pp,
which is the
fraction of photons emitted into the lasing mode. Inclusion of a gain medium in a
microcavity resulting in a large
@sp improves
the performance of a laser. The laser is more
energy efficient and exhibits a smaller threshold current (which will be described once a
more uncommon definition of threshold is introduced). Microcavity lasers have much
smaller turn-on times [10]. Below threshold, the light intensity increases from
spontaneous emission, so by increasing the spontaneous emission rate into the lasing
mode, the laser turns on faster once an input current is applied. Microcavity lasers also
Although photons are particle-like in that photons exchange discrete quanta of energy with atoms, photons
are wave-like in that photons must fulfill the boundary conditions of their surroundings [15]. Consequently,
photons can only exist by occupying a particular electromagnetic mode whether it be a free-space or a
resonant mode. Thus, one can never identify the exact location of a photon.
2
21
T
exhibit shorter turn-off times due to a reduced photon lifetime within the cavity that is
caused by a higher mirror loss rate. Finally, since spontaneous emission into non-lasing
modes ultimately sets the noise limit of a laser, microcavity lasers have been shown to
have less noise both theoretically [11], and experimentally [12].
R.T.
EXCITATION 2 kW / cm;
EFFECTIVE CAVITY LENGTH
144pm
0
x<4
52
0
4M
102
~m
'4
Z0-
WAVELENGTH
( nm )
Figure 5: Photoluminescence spectrum of Fabry-Perot cavities of different axial lengths. The light is
detected from the cavity axis. As the dimensions of the cavity decreases, light is more likely to be emitted
into the lasing mode. Figure is taken from [9].
2.4.2. The quantum-mechanical view of spontaneous emission: Vacuum
fields
As mentioned from the simple mode counting arguments, spontaneous emission
both "seeds" and "bleeds" the optical resonator [13]. However, the previous section did
not explain how an atom can "feel" the effects of it surroundings when placed in a
microcavity so that the "seeding" of light into the lasing mode is more potent. The
22
previous section also did not explain such effects as lasing without population inversion,
reversibility which thwarts the carrier "bleeding" process, or spontaneous emission
enhancement/inhibition where the rate of spontaneous emission into a mode is altered.
The goal of this section is to explain these phenomena by giving a physical picture of
how atoms and fields are inherently coupled, and how this coupling becomes noticeable
in a microcavity. The final conclusion will be that spontaneous emission can be tailored
and controlled, and hence is not very spontaneous at all.
Vacuum Fields in Cavity QED
Much like a golf ball at the top of a hill, an electron occupying an excited energy
level of an atom, or lattice, will remain there until another system interacts with it, even
though a lower energy level is energetically favorable [14]. In the case of spontaneous
emission, an electromagnetic field mode corresponding to the atom's transition frequency
must be present to induce an emission event. This might appear contrary to the
description of spontaneous emission offered by Einstein, where he showed that the
spontaneous emission rate, Rsp, is proportional to the number of excited atoms and is
independent of the number of photons through the following equation [15]:
dN
Rp=dt spoilt.=
A1
where A 2 1 corresponds to the spontaneous emission probability (sec- 1), and N is the
number of excited atoms. If the above equation is indeed true, then even without photons
present, spontaneous emission will still take place giving the false impression that a
medium does not require any outside influence in order to spontaneously emit a photon.
23
However, the Einstein coefficient, A 2 1, contains information about the outside world, and
in particular, the effect of vacuum fields which exist even in the absence of "real"
photons [15]. The vacuum, or zero-point, field is responsible for half of the spontaneous
emission rate [15] meaning,
1
Avac =- A21
2
(2)
where Avac is the transition probability per unit time due to the vacuum field. The vacuum
field is the electromagnetic field present in all space in the absence of photons. Its
existence is verified when one treats an electromagnetic field mode quantum
mechanically and quantizes it in terms of creation and annihilation operators [15].
Realizing that a monochromatic field mode is mathematically equivalent to a harmonic
oscillator, one arrives at the following equation for the oscillator energy levels.
E, =
h
c
n+--
2(3
Where n is an eigen-number representing the number of photons present in the mode
oscillating with angular frequency, o. The above equation reveals that even without
photons present (n=O), there is still a finite energy of 1Ahal present in the mode. This is
the zero-point energy of the harmonic oscillator which must be attributable to a field with
zero-mean, (otherwise the intensity could be viewed with a detector) yet with non-zero
fluctuations in time [13]. These vacuum fluctuations, or vacuum fields, are what induces
spontaneous emission. Accounting for the infinite number of frequency possibilities, one
arrives at the conclusion that the vacuum field can be thought of as an infinite "bath" of
energy [15]. Nonetheless, since energy is relative, one can mathematically set the vacuum
energy of a mode to zero although its affects cannot be eliminated 3 .
24
However, the vacuum field only accounts for half of the spontaneous emission
probability, the other half comes from the radiation's reaction field, a classical
phenomenon [16], which is the reaction of the atom to its own oscillations, similar to the
recoil of a gun. Thus, for the radiation reaction component of A 2 1 one can write,
Arr= Avac =-
1
2
(4))21
Addition of the radiation reaction and vacuum component preserves the total spontaneous
emission rate given in equation (1). Interestingly, the radiation reaction field is the reason
why there is no such thing as spontaneous absorption as the radiation reaction field can
only induce downward transitions; it exactly cancels the upward transitions of absorbed
vacuum field quanta [15].
With the existence and role of the vacuum field confirmed, spontaneous emission
is simply stimulated emission under the influence of the vacuum field [17] meaning that a
spontaneously emitted photon is in phase with the perturbing vacuum field. So in
reducing the number of vacuum states in a microcavity, one simultaneously eliminates
spontaneous emission into unwanted modes. Thus, the vacuum field couples the cavity to
the medium. By properly designing a cavity, one can judiciously eliminate vacuum field
modes and thus carrier loss by spontaneous emission into non-lasing modes. Hence,
mirrors play a different role in microcavity lasers than conventional lasers. Rather than
providing optical feedback for stimulated emission, the mirrors prevent unwanted
vacuum field modes from inducing spontaneous emission into unwanted optical modes.
If one embeds a narrowband medium, such as quantum dots or quantum boxes in
a properly designed microcavity, not only is the probability of coupling into the lasing
mode increased, the spontaneous emission rate into the lasing mode as compared to free
3 Another effect besides spontaneous emission is the Casimir Effect [15] whereby two conducting
plates are attracted to each other.
25
space is enhanced [18]. This phenomenon, known as the Purcell Effect [19], can be
explained with the vacuum field as follows: By reducing both the number of vacuum
states and emission bandwidth of the medium, a resonance condition between the vacuum
field and the emitting medium is created, where both systems oscillate at the same
frequency. In the case of a narrowband medium in a large cavity, the resonance condition
is not met, because vacuum fields of the correct frequency, but associated with non-lasing
modes, can induce emission thereby reducing the instances per second (rate) at which
atoms emit into the lasing mode. Conversely, an emitter with a large spectral width in a
microcavity can only exhibit a modest Purcell Effect, because the vacuum mode is still
4
unlikely to find an atom in a state corresponding to the correct transition frequency .
Minor Purcell enhancement is possible though, if the vacuum modes of the lasing
frequency are reduced, so that only the cavity mode can induce spontaneous emission.
To take the analysis one step further, if a narrowband medium is embedded in a
single mode cavity having negligible losses, the coupling between an atom and the field
becomes noticeably pronounced. In the strong coupling regime, energy is continuously
exchanged between the atom and the field [20]. With only one vacuum mode in the
emission linewidth of the atom, the atom can only emit into the cavity mode. However,
once the photon is generated, it resonates in the nearly lossless cavity, only to be
coherently absorbed by the atom. Instead of gradually decaying into a lower energy state,
the atom oscillates between excited and ground states at the Rabi frequency. Thus, by
properly engineering a cavity, spontaneous emission is a completely reversible and
controllable process. Rather than quanta of light flowing from the vacuum field into the
source field, it is periodically exchanged between the two [21]. This periodic exchange
4 This situation will result in an increase of the spontaneous emission factor though, because many
vacuum modes corresponding to non-lasing frequencies have been eliminated.
26
reveals the nature of photon generation and annihilation. A photon is never generated or
annihilated; it only transitions out of and into the vacuum field [15]. It is in the strong
coupling regime that these affects are apparent and new states of light can be generated
[12], making the engineering of quantum computers a possibility.
2.5. Other Photonic Crystal Lasers
The potential for creating efficient microcavity lasers using photonic crystals has
been recognized ever since the possibility of a photonic crystal was first reported [5].
Since then, several groups have reported lasing in photonic crystal lasers. In fact, since
the Distributed Bragg Reflector (DBR) mirror stack in a Vertical-Cavity SurfaceEmitting Laser (VCSEL), is essentially a one-dimensional photonic crystal, photonic
crystal lasers are not necessarily a new technology [3]. Indeed, a microcavity oxideconfined VCSEL has yielded a record low threshold current of just 8.7piA [22,23].
VCSELs naturally have good thermal management, so microcavity VCSELs can achieve
continuous-wave (CW) operation. However, since VCSELs emit light vertically, away
from the plane of the chip, their integration with other optical components is very
difficult. Distributed Feedback (DFB) and DBR lasers emit in-plane and are known to
have low noise and single mode lasing. However, these lasers usually have threshold
currents in the milliampere range with no references found for DFB or DBR lasers
requiring microamp threshold currents. Thus, a niche exists for low threshold edgeemitting lasers. To construct a low threshold edge-emitting laser, light can be confined
laterally by use of photonic crystal mirrors. The remainder of this section focuses on lowthreshold photonic crystal lasers.
27
The difficulty of making an electrical contact to a microcavity without injecting
carriers into unwanted portions of a device causes electrically-activated photonic crystal
lasers to be less common than their optically-pumped counterparts. However, opticallypumped lasers have demonstrated microcavity proof-of-concepts such as low threshold
powers and high speed operation. For instance, Altug et al [24] has demonstrated
optically-pumped photonic crystal lasers with a delay time of 1.5 ps allowing the direct
modulation of a photonic crystal laser at rates approaching the THz range. The photonic
crystal laser, consisting of a single defect in a photonic crystal membrane, is shown in
Figure 6. Although the photonic crystal membrane was cooled to obtain these results, the
ultra-small cavity could enable high speed direct electrical modulation of the laser.
Figure 6: Top view of a single defect photonic crystal laser [24]. The defect is performed by removing a
single hole from a surrounding photonic lattice.
An electrically-activated laser was demonstrated by Park et al [25] with a
threshold current of just 260pjA operating at room temperature. To tackle the problem of
making electrical contact to a microcavity resonator, the two-dimensional photonic
crystal slab sits on a post of semiconductor material. Electrical injection is limited to the
area of the resonator by means of the p-i-n junction which limits the carrier flow to other
regions of the laser to length scales on the order of a diffusion length. Surface
28
recombination at the edges of the photonic crystal holes probably limits the threshold
current. The free standing structure might also be awkward to integrate with other
components on a chip. The electrical drive current was pulsed so CW lasing was not
demonstrated. Finally, because the photonic crystals strongly confine the light in the
plane of the chip, the laser is surface emitting [26], although the authors do not explicitly
state the laser's emission direction.
Figure 7: Electrically-activated photonic crystal laser demonstrated in [25].
Happ et al demonstrated a coupled cavity photonic crystal laser, shown in Figure
8, with a threshold current of l5mA using coupled cavities to form a waveguide for the
light [27]. The high threshold current is caused by the lateral diffusion of carriers to
regions outside of the coupled cavity waveguide. The coupled cavity waveguide photonic
crystal laser does achieve electrical activation and continuous wave (CW) lasing with a
coplanar output. However, the lasers are composed of around 40 microresonators and are
155pm in length, much larger than other photonic crystal-based lasers.
29
Figure 8: Coupled cavity photonic crystal laser [27]. The hexagonal features are microresonators within a
surrounding PBG lattice. Shown here are 3 of 40 total microresonators.
Zhou et al reported an electrically-activated laser-like structure that exhibited a
soft-threshold characteristic that is the result of a high spontaneous emission factor [26].
A single defect is incorporated into a photonic crystal and a distributed Bragg reflector
stack is used to isolate the optical mode from the bottom contact and the substrate. A
schematic of the device and the light-current performance of the device are shown in
Figure 9. In pulsed operation, a "soft" threshold current of 300gA is observed with a
maximum output power of 14.4pW. The soft transition at threshold is due to a large
spontaneous emission factor of I~zO.06. Since the carriers must traverse around manylithography defined holes to reach the active region, the device suffers from a large
amount of surface recombination at the hole edges. Also, since the photonic crystals
confine light in-plane, most of the light leaks out vertically and not in-plane.
44
2D PBG defect
p"lsed
P cntctI
3 -
1
0
1
0
2
Current (mA)
3
4
Figure 9: Schematic and output characteristics of the laser described in [26]. The device is isolated from
the substrate by an oxidized bragg mirrors stack. The oxidation front is stopped just before the defect, so
that current can be injected from the bottom contact. The soft threshold is shown in the inset of the L-I
curve.
30
Chapter 3.
Design and Simulations
3.1. Design Concept
From the reports in the literature, there is no work describing electricallyactivated, edge-emitting microcavity lasers. A fundamental problem with the design of
electrically-injected, edge-emitting, microcavity lasers is the placement of the contacts.
The difficulty lies in positioning the contacts, so that they only inject current into the
microcavity without interfering with the emitted light. The design of the laser
investigated here accomplishes electrical injection into a microcavity through the use of
crossing semiconductor beams and an undercut. Another problem with edge-emitting
lasers is the removal of the active material from the passive output waveguide, while still
maintaining a microcavity. The crossing-beam design presented below accomplishes this
by selective etching of the active material from the passive output waveguide. A
schematic of the laser and a simplified schematic of the epilayers for one particular
device used in this thesis are shown in Figure 10.
31
It
/
P-Contact
I
Gain Material
Figure 10: Schematic of the photonic crystal microcavity laser and generic epilayers.
The electrically-activated photonic crystal laser uses two crossed beams of
semiconductor material to create a microcavity. Holes are injected into the microcavity
from the top p-type beam and electrons are injected from the bottom n-type beam. The
crossing of the two beams defines the active area where the carriers ideally recombine
radiatively in the gain material residing within the top beam. Light generated in the gain
material is coupled into the bottom, output waveguide (shown in red in Figure 10). The
photonic crystals, which act as mirrors, are formed by patterning holes into each beam
except where they cross. The lack of holes creates a defect within each beam resulting in
a highly efficient resonator for frequencies residing within the photonic bandgap. Fewer
holes are patterned in one direction of the bottom waveguide, so that the emitted light
32
will be preferentially transmitted into the passive output waveguide in this direction.
Light is confined by index confinement in the vertical direction and by the photonic
bandgap in the axial direction.
The p and n-type regions are electrically isolated everywhere except in the active
region by the use of an undercut which removes the n-type material underneath the
regions of the top beam that are patterned. Without performing this undercut, the entire
device would function as a p-i-n diode and the benefit of forcing the electrons and holes
to recombine only in the active region would be lost. The undercut also reduces the
optical cavity volume by removing material that could otherwise contain part of the
optical mode. As mentioned in Chapter 2, a reduced cavity volume has many effects
including a reduction of the threshold current.
Thermally-oxidized AlAs is formed underneath the bottom waveguide to further
confine carriers and photons to the desired areas. Oxidized AlAs (AlxOy) serves as an
insulator so that a current path does not exist between the contacts via the substrate. This
parallel current path might lead to an unreasonably high threshold current if the resistive
path through the substrate is low. The oxidized AlAs also has a low refractive index
(1.55) which prevents the optical mode from leaking into the high refractive index
substrate.
The microcavity photonic crystal laser is well suited for integrated optics for
many reasons. The laser is electrically-activated eliminating the need for a separate pump
laser and the difficulty of focusing an optical pump beam on a microcavity-sized
structure. The photonic crystal laser is both practical and efficient; both the active and
cavity volume are small which leads to a small threshold current, high efficiency, high
33
speed, and low noise. The laser has a relatively small footprint, which conserves valuable
chip real-estate. Finally, the laser's output is fed directly into an in-plane optical
waveguide eliminating the need for couplers thus easing integration of the laser with
other components. Figure 10 shows how the output light beam leaves the microcavity in
the lower waveguide in the direction of the fewest holes, in this case, three holes.
3.2. Layered Structure Design
Many considerations were taken into account when designing the thickness and
composition of the epilayers. In an initial design, the output waveguide rested on the
absorbing active material making it incapable of guiding light with low loss. In later
designs, the laser structure was "flipped" so that the output waveguide resides just above
the oxidized AlAs layer and the active material is removed from above the output
waveguide.
In the initial microcavity laser designs, the top beam was referred to as a
waveguide, because it was thick enough to support a guided mode. In the current design,
the dimensions of the top AlGaAs cladding layer were reduced, so that the upper-beam
would be unable to support any optical mode of the light that is being generated by the
active medium. A trade-off is incurred however, because the top beam also contains the
gain medium. If an insufficient amount of light resides within the top beam, the modal
overlap with the gain material will be insufficient to support lasing. If too much of the
optical mode overlaps the gain material, the generated light will not couple into the
output waveguide as usable light. Thus, optical simulations were carried out to ensure
that the optical mode overlaps both the active medium and the output waveguide. These
34
modal simulations (section 3.2.1) were used to determine the thickness of the AlGaAs
cladding and the output waveguide.
The maximum vertical thickness of all the grown layers could not exceed 1.2gm
due to the maximum thickness (-1.8pm) of the Clariant AZ5214 photoresist that was
used in the fabrication the laser. This constraint limits the thickness of the underlying
aluminum oxide layer and hence the AlAs layer. Ideally, the AlxOy layer should be quite
thick (-1gm) in order to prevent light from coupling into the GaAs substrate. In the first
generation of grown wafers, sample VA28, the AlAs thickness was 1.0gm, but during the
fabrication of the microcavity laser, an AlAs thickness of 1.0pm was determined to be
too thick to insure adequate photoresist coverage. Two new generations of samples
(VA34 and VA35) were grown with an AlAs thickness of 0.5gm. The latest generations
incorporated many other changes which are explained below.
The first generation, sample VA28, included an InGaAlP-based output waveguide
with a high index, dilute waveguide core composed primarily of InGaP interspersed with
thin GaAs layers. The high index core serves to "pull" light down into the output
waveguide from the upper active region. Although InGaAlP provides an output
waveguide whose index of refraction is slightly lower than Alo.5Gao.5 As, InGaAlP is
difficult to etch using the reactive ion etchers at M.I.T. Subsequent samples (VA34 and
VA35) used a thick layer of InGaP for the output waveguide material.
Phosphide-based material was used as the output waveguide primarily for two
reasons. First, materials such as InGaP or InGaAlP are known to have less optical loss
than GaAs or AlGaAs [28]. Secondly, the significant etch selectivity between phosphidebased and arsenide-based materials is necessary for the undercut step.
35
Schematics of the final grown wafers are shown in Figure 11. All of the wafers
were grown in the Veeco GEN 200 Molecular Beam Epitaxy (MBE) system in the
Nanoprecision Deposition Lab. MBE can provide high crystalline quality III-V epitaxial
films of precise thicknesses.
Grown Structure: VA28
1Onm p-GaAs: Be C
20nm GaAs
8nm In o.15GaO.85As
0.85nm InAs
20nm GaAs
8nm InO.1 5GaO.85As
0.85nm InAs
70nm n-InO. 5GaO. 5P: Si
10nm n-GaAs: Si
20nm GaAs
25nm AlO. 5GaO. 5As
20nm n-In0 .53GaO. 47P:
Si
70nm n-InO. 5GaO. 5P: Si
10nm n-GaAs: Si
70nm n-InO. 5GaO. 5P: Si
36
Grown Structure: VA34
10nm p-GaAs: Be
I15nm
GaAs
8nm InO.1 5GaO.85As
15nm GaAs
8nm InO.15GaO.85As
15nm GaAs
25nm AlO.4 8GaO. 52As
Grown Structure: VA35
10nm p-GaAs: Be
40nm GaAs
6nm In 0 .15GaO. 85As
0.85nm InAs
2nm In 0 .15GaO. 85As
10nm GaAs HighT
5nm p-GaAs:Be HighT
20nm GaAs HighT
5nm GaAs
6nm InO.1 5GaO. 85As
0.85nm InAs
2nm InO.1 5GaO. 85As
10nm GaAs HighT
5nm p-GaAs:Be HighT
20nm GaAs HighT
5nm GaAs
25nm Al0.48Gao. 52As
Figure 11: Schematics of the grown epiwafers.
Since different gain regions have different advantages, several were grown.
Quantum dots are formed by the growth of highly lattice-mismatched InAs on GaAs or
low In content InGaAs. Due to the lattice mismatch strain, the InAs forms small islands
37
of material during the first few monolayers of growth. The overgrown InAs islands
confine carriers in three-dimensions causing the carriers to occupy very specific
electronic states (much like a microcavity). The number of electronic state possibilities
for a given energy per unit crystal volume is given by the density of states function, p(E).
The discrete density of states caused by carrier confinement in quantum dots is expected
to produce a very narrowband emission spectrum, allowing greater Purcell enhancement
as mentioned in Chapter 2. The discrete density of states also means that the injected
carriers quickly thermallize to energy levels that are resonant with the cavity photons.
The high differential gain, dg/dN of quantum dots decreases the turn-on time of the
semiconductor lasers. Both samples VA28 and VA35 were grown with quantum dots
buried inside an InGaAs quantum well. However, sample VA35 was grown so that the
InAs quantum dot layer was sandwiched between two InGaAs layers as opposed to being
grown on top of a GaAs layer. Sample VA35 also incorporated high temperature GaAs
spacer layers and Be-doped GaAs barriers to improve the quantum dot quality [29].
Strained quantum wells are a well-studied active material with many advantages
over unstrained quantum wells. Most notable is the reduction in Auger recombination due
to an increased valence band curvature [7]. The strained quantum well in sample VA34 is
an 8 nm thick InO15GaO. 85As layer surrounded by GaAs barriers. Although sample VA34
was designed to ideally emit light at 980nm, a wavelength that is not applicable to
integrated optics, sample VA34 was incorporated into one of the microcavity laser
designs to prove the concept of the microcavity laser.
The photoluminescence (PL) spectra for all of the structures are shown in Figure
12. The PL spectrum is measured by exciting a sample with a laser emitting photons with
38
an energy above the bandgap energy and by observing the emitted light from the sample
due to spontaneous decay. The PL spectrum shows the emission behavior of the sample
without the effects of the laser microcavity. From the figure, the strained 8 nm thick
In0 .15Gao. 85As quantum wells (sample VA34) are observed to have the narrowest emission
spectrum and emitted at 960nm. The 980nm emission peak in sample VA28 is due to the
InGaAs quantum well covering the InAs quantum dots. The emission peaks from the
quantum dot layers occurred at -1050nm in sample VA28 and -1245nm in sample
VA35. The broad emission spectrums of samples VA28 and VA35 is due to the spread
in quantum dot sizes which leads to a broader density of states and thus a broader
emission spectrum. For this reason, experiments in the strong coupling regime usually
utilize as few quantum dots as possible.
Grown Structure PL Data
4.5
4
373.5
-
S3
.
-VA28
2.5
-
-
VA34
-
VA35
1.5-1
0.50
700
800
900
1000
1100
1200
1300
1400
1500
1600
Wavelength (nm)
Figure 12: Photoluminescence data for grown epilayers
3.2.1. Optical Simulations
39
Design software from Optiwave was used to ensure a proper modal overlap
between the various sections of the lasers and the optical mode. The program uses the
beam propagation method (BPM) to calculate the electromagnetic field behavior as light
traverses a device. The Optiwave BPM software assumes paraxial rays and does not take
backward reflections into account. A detailed explanation of BPM can be found in [30].
Using a cross-section of the microcavity laser, the transverse electric field distribution of
the guided mode was analyzed
The index of refraction of most of the materials was taken from [31]. If the index
was not given for a particular alloy, a superposition of the index of refraction of known
alloys was used. The index of AlGaAs was found by using a numerical equation found in
[32]. The code that was used to determine the index of refraction of AlGaAs is found in
Appendix 1. The index of refraction of all layers was assumed to be constant with carrier
density. Each device width was set to 600nm as this width resulted in a waveguide with
single guided mode. Figure 13 shows the simulated horizontal component of the guided
electric field for each structure. Since the electric field is perpendicular to the direction of
propagation, this is referred to as the Transverse Electric (TE) polarized mode. As seen
from the guided modes, the fundamental mode overlaps both the gain material and the
output waveguide in all cases.
40
Grown Structure: VA34
Figure 13: Grown structures and their transverse fundamental mode distributions.
3.3. Rate Equation Calculations
One goal of this thesis was to theoretically predict the behavior and relevant
figures of merit for the laser herein. The phenomenological rate equation model found in
[7] is used. The rate equations for the carrier concentration and photon density can be
written as:
dN
dt
CN 3 - BN
I_
V
=iq
dN
2
- AdN - AsufN -vg V
-
E=g
I1
g Np+
V
gN)
(5)g~
I2
,,PB N2-9 < a > NP
t
>P
(6)
where N is the free carrier density in the active region (cm-3), and Np is the lasing mode
photon density in the laser cavity (cm- 3). The physics behind each term as well as the
V
values for each constant are given in Appendix 2. The term, -
IF, that is present in the
carrier rate equation is different than in reference [7] and most other texts because V, is
defined as the physical photon cavity volume rather than the modal volume as in other
books. The factor Vp/V accounts for the fact that photons occupy a greater volume than
41
the active material and the factor, F, accounts for the non-uniform energy density
distribution that photons must satisfy in a cavity. This notation is used to stress that if
there is no modal overlap with the active region (F=0), then there can be no stimulated
emission. This term is not present in the spontaneous emission term, because even if the
lasing mode does not overlap the active region, other vacuum modes can still cause
spontaneous emission.
Since, the time dynamics of the laser are not being analyzed, the laser is assumed
to be in steady state meaning that the time derivatives in the above rate equations are
zero. When equation (6) equals to zero, the density of lasing-mode photons in the cavity
is given by the following equation [33].
1'g<a>
1g
(7)
Equation (7) is the driving equation for laser action. Physically, it shows that there
are two processes responsible for laser action: Stimulated emission in the denominator,
and spontaneous emission in the numerator. The denominator contains the loss minus the
gain due to stimulated emission in the lasing mode. The gain can never equal the loss
otherwise the photon density will be infinite [33]. In fact, as the gain asymptotically
approaches the loss, the photon density in the lasing mode increases and laser action is
observed. This is in contrast to the normal method of defining threshold as the point
where gain equals loss, a case which can not exist.
The numerator in equation (7) is the spontaneous emission rate into the lasing
mode. For conventional lasers where Ppp is small, the numerator is very close to zero, and
the gain can be very close to the loss without introducing any singularities. In
42
microcavity lasers, psp can be quite large meaning that spontaneous emission can also
drive laser action. Moreover, in microcavities, the gain can be much smaller than the loss
and Np can still be large enough for linewidth narrowing to be observed- the hallmark of
laser action. If
psp is
large enough, the material gain, g, can be less than zero (no
population inversion), and there can still be a substantial amount of photons present in the
lasing mode! Hence, the phrase "Lasing without population inversion." [34]. This can be
physically understood by recognizing that even though the medium is absorbing photons
(since the gain is less than zero), there is a good probability of re-emitting the photons
into the lasing mode. Consequently, no measured loss of lasing-mode photons is observed
[13]. Usually laser action is characterized by a dramatic change in efficiency at threshold
once stimulated emission becomes dominate. For high psp, the numerator plays a larger
role and the change in efficiency is less or not noticeable at all as in the case of a
thresholdless laser.
The photon modal loss (cm-)
can be separated into two loss terms acting
simultaneously: the internal loss, and light lost from the photonic crystal mirrors, some of
which is useful.
<
a>
=
< C > + < am >
(8)
The output power is given by,
Pout= Fvg < a,, > hf Np Vp
(9)
where F is the proportion of photons exiting the output photonic crystal mirror as
compared to the opposite mirror. Multiplication by the photon volume converts the
photon density lost due to the mirrors per unit time to the actual number of photons being
emitted per unit time. Note that equation (9) explicitly illustrates the direct dependence of
the output power on the cavity volume. In general, the larger the cavity, the more photons
43
the cavity can store, and thus the more photons that the cavity is capable of emitting per
unit time. So while microcavity lasers might have many benefits, they will not be useful
for any high power applications, unless an array of lasers is used.
Since data was readily available, the material parameters for strained quantum
wells were used for all material dependant values in the simulations [7]. A wavelength of
960nm, corresponding to the emission peak of the grown strained quantum wells sample,
was assumed. Because the Optiwave software package can not calculate the confinement
factor, it was set to V/V.
Future modal calculations should use a program that can
calculate the confinement factor, so that more accurate results can be obtained. If the gain
is assumed independent of polarization, the confinement factor is simply the photon
energy in the gain material divided by the photon energy in the entire cavity.
Although
3ps
is the
most important factor for microcavities, it is also the most
difficult to calculate. Several groups have calculated
3p,
for different cavities, but the
calculations are quite involved [35,36,37,38]. Thus, the spontaneous emission factor is
parameterized in the calculations. A spontaneous emission factor of 0.01 is expected from
measurements on micropost VCSELS [39], which are similar to this laser in terms of
light confinement. Nonetheless, 1 sp is varied from 0.005, a worst case scenario calculated
by Erchak [40], to 0.05, a best case scenario measured in [26].
Using methods, which are further explained in Appendix 2, light (power) versus
input current (L-I) curves were calculated. Figure 14 illustrates the results and shows that
the output power is predicted to be small - on the order of micro-amps. This does not
include coupling losses from the laser into the output waveguide, or propagation losses as
the light propagates through the waveguide. Detecting the light will be difficult with a
44
fiber connected to a detector. For this reason, lasers integrated with photodetectors were
added to the mask design, so that light could be detected without worrying about extra
coupling losses.
74
Power vs. Injection Current
1
sp=. 0 5
6-
=. 0 4 1
5
Psp.032
4-
1 sp. 014
2-
1
0
0
0.2
~
~
0.4
0.6
Injetion Cirrent (A)
Figure 14: L-I curves for the photonic crystal microcavity
1=.005
_.-
1
0.8
X 10
laser.
In microcavity lasers, the conventional way of defining threshold as the point
where gain equals loss is no longer valid. It can be shown, from Einstein's treatment, that
the spontaneous emission rate into the lasing mode equals the stimulated emission rate
when there is one photon in the lasing mode [41]. Since threshold is the point where
stimulated emission begins to dominate spontaneous emission (this occurs when
linewidth narrowing is observed), threshold can be rigorously defined as the point where
there is one photon in the cavity [42]. Only when NpV=1, a photon survives long enough
45
to induce other stimulated emission events. Using this definition, the threshold injection
currents for the above six cases were determined and are shown in Table 1.
P
0.005
446
0.014
0.023
133
0.032
106
0.041
89
193
r1i'th (PA)
Table 1: Calculated threshold injection currents for the photonic crystal microcavity laser.
0.05
79
The calculated threshold injection currents are in good agreement with the 300piA
terminal current observed in [26] and the 260pA terminal current observed in [25]. For a
reasonable injection efficiency r1, and a reasonable spontaneous emission factor, Psp, the
proposed microcavity laser could yield the smallest threshold current for an electricallyactivated photonic crystal laser to date. The laser will undoubtedly yield the smallest
threshold current for an electrically-activated edge emitting laser.
3.4. Mask Design
In total, nine masks are required to fabricate the photonic crystal microcavity
laser. In Chapter 4, a fabrication sequence is presented which incorporates only a single
electron-beam lithography step. Because photolithography is used in lieu of electronbeam lithography in the fabrication sequence, a large burden rests on the proper design of
the optical masks.
Great care was taken to design a mask set that simplifies both fabrication, and
testing. A step and repeat design is used so that many lasers with varying dimensions can
be fabricated at once. A die measuring
/4"x
/4"
contains 208 lasers each with varying
features allowing one to empirically determine the optimal laser. To facilitate electronbeam lithography, arrays of 6 lasers are fabricated within a 200pjm x 200pim electronbeam field, the area the electron beam can access without moving the sample stage. This
46
also simplifies testing, because a fiber connected to a detector will only need to be
displaced by more than 35pm after every
6 th
laser. In addition, arrays of lasers have
practical applications in telecommunications. The output waveguides are angled by 70
relative to the cleavage plane to prevent reflections from the output facet. The contacts
are distributed so that only one probe needs to be moved after testing each laser. Many
diagnostics are included and are shown in Figure 15.
Some of the more important
diagnostics are described in the section that follows.
A.)
6X6 die set included
in each 4" mask
B.)
Resistance
tests
Etch tests
3 Rows of PC Laser
Unit Cells
}
PC lasers with output
sent to an integrated
Photo-detector
Large area photo-detector
}
}
2 Rows of stripe Lasers
cleaved to Varying lengths.
Stripe Laser With Passive
section cleaved to various
lengths.
Optical waveguides
47
C.) Unit Cell
I
Cleave Line
P-type contacts
N-type contact
D.) Laser Array
48
E.)
Figure 15: Mask views with varying zoom levels. The red ovals indicate the region shown in the
subsequent zoom level. A.) The entire step and repeat mask includes 36 identical dies, B.) Each die consists
of 234 lasers of varying dimensions and many diagnostics. C.) Each unit cell on the die contains 12 lasers
and accompanying contacts. D) An array of 6 lasers each separated by 30pm. E.)Each laser requires 8
masks to fabricate.
3.4.1. Stripe Laser Diagnostic
One advantage of optical lithography is the easy incorporation of diagnostic
devices without additional fabrication effort. While the incorporation of diagnostic
devices complicates the optical mask design, their utility should warrant the extra time
spent during the design phase.
One such diagnostic device is a stripe laser which is used to test the quality of the
lasing material and serves as an important verification of the design before commencing
the timely electron-beam lithography step. The stripe lasers consist of six rows of stripes
that can be cleaved to various lengths to form cleaved facet lasers. The lasers are simple
stripe-loaded waveguide structures with contacts for carrier injection. The stripe ridge can
be viewed as a region with a large effective index within a slab waveguide and thus
confines the fundamental mode to areas directly below the ridge. Ridge widths of 2, 4,
49
and 6gm are included on the mask. A schematic of a single stripe laser is shown in Figure
16. The upper p-type material is colored purple while the lower n-type material is colored
in red. The p-type contact is highlighted yellow; the lower n-type contact is highlighted in
blue. Cleaved facets are used as mirrors. An undercut is also necessary to isolate the p
and n type regions but unfortunately requires an extra fabrication step.
Figure 16: Schematic of a single stripe laser diagnostic device.
Also included in the mask design are stripe lasers integrated with a passive
waveguide. By offsetting identical structures in the mask design, at least two stripe lasers
with identical active lengths, yet non-identical passive lengths, will result after cleaving.
By comparing the output characteristics of each laser one can then determine the loss in
the passive section.
ire 17: Mask layout of stripe laser with integrate passive section
50
3.4.2. Integrated Diagnostic Detector
Since the output power of the photonic crystal microcavity laser is predicted to be
quite small, an integrated diagnostic detector was included in each of the mask dies. As
seen in Figure 18, the detector appears much like the photonic crystal laser except that the
holes are entirely removed from the input. However, holes are included on the opposite
side, so that the detected light will reflect off the photonic crystal mirror effectively
doubling the absorption length in order to increase the sensitivity of the detector. Also,
the detector incorporates a wider upper p-type beam to increase the detector's absorption
length. Finally, a slice of material is removed from the input side to electrically isolate
the reverse biased detector from the forward biased laser. Since this slice is included in
the electron beam mask, it can be placed anywhere between the detector and laser
without modifying the optical photolithography masks. The total distance between the
photonic crystal laser and the integrated detector is 100pm. In comparison to the standalone photonic crystal laser, the length of the output waveguide is 200pm.
Figure 18: The integrated diagnostic photodetector
51
Chapter 4.
Fabrication
4.1. Fabrication Sequence
Due the complicated nature and time required for electron-beam lithography, the
aim of the fabrication sequence is to pattern all of the small features with a single
electron-beam lithography step and to reduce the time required for the electron-beam
lithography step. The first criterion is accomplished by using conventional, contact
photolithography to pattern all of the large features such as the electrical contacts, and by
using electron-beam lithography to only trim the large features. The second criterion is
met by placing 6 lasers within a single electron-beam lithography field, and again by
using electron-beam lithography only for small features. Consequently, most of the
fabrication sequence uses standard photolithography. While the proposed hybrid
lithography scheme increases the time spent during the design phase because more
processing steps are required, it allows for a process flow consisting of mostly simple
photolithography and etch steps. Finally, due to the use of contact lithography, all the
features across a wafer can be patterned during one exposure allowing many variations of
the laser to be incorporated easily onto a single wafer.
Figure 19 summarizes the fabrication sequence. Standard photolithography and
lift-off processes are used to define the electrical contacts. Depositing the contacts on a
bare substrate leads to better ohmic contacts, since fabrication damage to the surface is
52
1
minimized prior to the deposition of the ohmic contact metal. Depositing the metal first
also creates highly visible base alignment marks. Previous work [43] revealed that
alignment to previously defined features became difficult during subsequent electronbeam lithography steps due to the absence of metal alignment marks. Furthermore, metal
base alignment marks allow one to consistently align each mask to the same feature
eliminating the deviations that often accompanies alignment to progressively defined and
created features.
A series of photolithography steps and III-V material etches are used to define the
contact mesa, the upper p-type cross beam and the n-type lower passive waveguide. A
hybrid electron-beam lithography and photolithography approach is used to define the
submicron features of the photonic crystals and the microcavity. Finally, via openings
through a protective dielectric layer, an undercut of the upper waveguide and an AlAs
oxidation process step are performed. In general, entire two inch GaAs wafers were
fabricated. Within the process flow, diagnostic stripe lasers can be created and tested to
ensure that the gain medium is capable of emitting at the desired wavelength.
53
1.) Deposit and Pattern Photo resist
3.) Pattern Resist to Define P-type beam
5.) Pattern Resist For N-type Metal
2.) Apply and Lift-off P-type metal
4.) Wet Etch to Phosphide Remove Resist
6.) ADDlY and Lift-off N-Metal
8.------and Pattern Photo resist
7.) Deposit PECVD oxide
9.) Etch Oxide
10.) Remove Resist Dry etch to substrate
Undercut and test Stripe Lasers
--------------------------------------I
54
11.) After a combination of E-beam and
optical lithoaraohy
12.) Perform 3 RIE etches to substrate
13.) Apply and Pattern Resist for
undercut
14.) Undercut and Remove Resist
15.) Open up vias to Contacts
16.) Oxidize bottom AIGaAs then test
Figure 19: Fabrication sequence for the electrically-activated microcavity laser and the diagnostic stripe
laser. Steps 8-10 are only required to fabricate the diagnostic stripe lasers before electron beam lithography,
or focused ion beam etching.
4.2. Fabrication Results
4.2.1. Steps 1-2: Formation of ohmic contacts on p-type arsenide-based
material
A good ohmic contact is critical to obtain a low-power laser. A contact
with a large contact resistance can be viewed as a resistor in series with the diode laser.
Although the contact resistance does not affect the threshold current, it does affect the
voltage required to reach Ith and thus the input power. In addition, the power dissipated
across the ohmic contact heats the laser which degrades the optical performance of the
laser.
55
Whenever a metal and a semiconductor come into contact, the Fermi-levels in the
semiconductor and in the metal align so that an equilibrium is reached. The difference in
the free charge and the electron affinity between the metal and the semiconductor, results
in a built-in electric field and thus a potential barrier (much like a p-n junction) [44]. A
good ohmic contact occurs when the tunneling current is much larger than the thermionic
emission current over the built-in potential barrier. The band alignment between a metal
and a semiconductor, along with the associated potential barrier,
OB,
is shown in Figure
20. Low resistive ohmic contacts are achieved by heavily doping the semiconductor at
the interface to reduce the width of the barrier and by choosing a metal with an electron
affinity close to that of the semiconductor to reduce the height of the potential barrier
[45]. Since tunneling is a linear process, an ohmic contact results in a linear I-V
characteristic.
A.) Thermionic emlsslmn
electrcm
L) Tunnelhng
Figure 20: A) The band diagram and potential barrier associated with thermionic emission. B) The band
diagram and potential barrier associated with carrier tunneling.
Several metals were considered to make an ohmic contact to a 10nm thick,
heavily doped contact layer of GaAs:Be with a 125nm thick AlGaAs:Be cladding layer
underneath. The Au/Mn/Ni/Au structure has been found to have an extremely low contact
resistivity of 1.6x10-8 Q cm 2 [46], but Mn is not available in the NanoStructures
Laboratory (NSL). Another contact that exhibits good adhesion and excellent surface
morphology due to the absence of Au is based on the Ni/Zn/Al system [47]. However, a
56
self-aligned contact is used for the diagnostic stripe lasers, resulting in the ohmic contact
metal being left unprotected by photoresist during the etching of the arsenide-based
material. Since AlGaAs is etched, an Al-containing contact might not withstand the wetetch. In light of these limitations, the Au/Zn/Au multilayer structure was chosen. The
Au/Zn/Au structure has been shown to have a contact resistance of 3x10-60 cm 2 and to
have good adhesion to p-GaAs [48]. Since the thickness of the epilayers was a concern
for sample VA28, a Au(300A)/Zn(370A)/Au(830A) ohmic contact metallization scheme
was
used.
Subsequent
samples
utilized
a
contact
structure
consisting
of
Au(300A)/Zn(370A)/Au(2000A) as recommended in [48].
A lift-off process was used to pattern the p-type ohmic contacts. Clariant AZ5214
image reversal photoresist was used in step 1. Image reversal photoresists are used in liftoff processes because these photoresists provide inward-slanted sidewalls, which allow
solvents to penetrate between the metal layers and the photoresist during the lift-off
process. The most reliable photolithography process in the Technology Research
Laboratory (TRL) for lift-off processes is outlined below.
AZ5214 photoresist image reverse process
Solvent Clean: Acetone, Methanol, Iso-propanol
HMDS 30 minutes: Recipe 5 in TRL
Allow wafer to cool for 3 minutes
Coat Wafers:
Dispense: 500rpm, 6 seconds
Spread: 750rpm, 6 seconds
Spin: 4000rpm, 30 seconds
Prebake: convection oven at 95' for 30 minutes
Expose using EV1 contact aligner for 1.5 seconds
Alignment Seperatation: 30pm
Contact Mode: Hard Contact
Mask Thickness: 1.6mm
Substrate Thickness: 352pm
Reversal Bake: convection oven at 95' for 30 minutes
Flood Expose on EV1 for 60 seconds
Develop in AZ422 developer for -100 seconds
57
Prior to metallization, all of the samples were descummed in NSL to remove any
residual resist from step one. The descum process consists of a plasma of helium and
oxygen which removes any organics such as photoresist from the surface. Details of the
descum process are listed below. Following the descum process, the ohmic contact metals
were evaporated onto the samples using the NSL electron beam evaporator. Due to the
high vapor pressure of Zn, the system pressure was kept at, or below 2x10~6 Torr during
the metal deposition [48].
Descum process in NSL Plasmatherm
First clean the chamber for 4 min. using a CF 4/0 2 Plasma
Descum sample in He/0 2 Plasma
Chamber Pressure: 7mtorr
He flow rate: 5sccm
02 flow rate: 1 Osccm
Power: 150W
Time: 20 sec after plasma sparks
After metallization, lift-off was performed in NSL using a hot N-methyl
pyrimidinone (NMP) process. After heating the NMP to 130C using a hot plate, each
sample was placed in the solution and gently stirred for a duration lasting between 15-30
minutes. The process consistently removed the unwanted metal and photoresist on each
sample. Examples of metal features are shown in Figure 21. As will be mentioned later,
alternative alignment marks should be included for better precision.
58
A.) Unit Cell
B.) Alignment Marks
C.) Vernier Mark
Active Region
Vernier Marks
Figure 21: Metal features after steps 1-2. A) A unit cell containing 6 active regions. B) Alignment marks
C) Vernier alignment marks as viewed with a 50X objective. Each line is 1.5pm wide with a minimum
spacing of 1.5pm between each line.
4.2.2. Steps 3-4: Wet-etching of Arsenide based material
The purpose of steps three and four is to pattern and etch the upper arsenide-based
material. The arsenide-based material in the active regions will eventually be trimmed
during the electron-beam lithography and subsequent etching process steps. Removing
the upper arsenside-based material allows the electrical contacts to the bottom phosphidebased material to be created. The ridge of the stripe diagnostic laser is also formed during
the etching of the arsenide-based material with the p-type ohmic contact metal serving as
a self-aligned etch mask.
The resist pattern in step 3 was formed by using Clariant AZ5214 photoresist as a
positive resist. The positive AZ5214 resist process produces sidewalls with lower
roughness than the Arch Chemical OCG 825 photoresist; the more commonly used
positive resist in TRL. Smooth sidewalls are necessary for acceptable stripe lasers. The
details of the AZ5214 positive resist process is listed below. After patterning, the wafers
were descummed using the same process that was described in step 2, except the plasma
was terminated 10 seconds after the plasma ignition. By removing just a very thin layer
of resist, the descum process decreases the photoresist sidewall roughness.
59
AZ5214 photoresist positive process
Solvent Clean: Acetone, Methanol, Iso-propanol
HMDS 30 minutes: Recipe 5 in TRL
Allow wafer to cool for 3 minutes
Coat Wafers:
Dispense: 500rpm, 6 seconds
Spread: 750rpm, 6 seconds
Spin: 4000rpm, 30 seconds
Prebake: convection oven at 95* for 30 minutes
Expose using EV1 contact aligner for 10 seconds
Alignment Seperatation: 30pm
Contact Mode: Hard Contact
Mask Thickness: 1.6mm
Substrate Thickness: 352pm
Develop in AZ422 developer for -100 seconds
Vacuum cure: 15 min. 10- torr
Following resist patterning, the arsenide-based material was etched in a solution
of 1:1:10, H 2 SO 4 :H 20 2 :H 2 0 [49]. The reaction was fast and uncontrollable with features
even 10pm in width being completely undercut. Although 10ptm features were being
undercut, the sulfuric acid/hydrogen peroxide-based solution preferentially etches
arsenides as opposed to phosphides so that the etch depth equals the total thickness of the
arsenside-based layers which is sample dependent. In an attempt to minimize the
undercutting, the solution was diluted with deionized water and its temperature was
controlled through the use of a room temperature water bath [50]. The water bath
removes the heat that is generated from the exothermic reaction that occurs when sulfuric
acid and hydrogen peroxide are diluted with water. Upon mixing the chemicals,
approximately 20min is required for the solution and the water bath to reach the same
temperature of 25±2'C. A final concentration of 1:1:40 H 2 SO 4 :H 2 0 2 :H 2 0 resulted in an
etch rate of -26A/sec as measured by dipping a cleaved test wafer into the solution for 10
seconds per dip and then by measuring the resulting etch depth using a surface
60
profilometer.
A general observation was that identical measurements could vary by
about 200A, so several features were measured to determine an average etch rate.
A.) Active Area
B.) Unit Cell
Figure 22: Photonic crystal laser features after removing the p-type material. A.) The active area of a laser
with the patterned p-type beam defined. B.) A unit cell depicting a total of what will be 12 lasers. Compare
to figure 15 (c).
4.2.3. Problems with Metal Adhesion
Although a usable wet-etch process was developed for the photonic crystal lasers,
some critical problems with metal adhesion were revealed during this step. In particular,
the metal on the alignment marks and stripe laser ridge were removed during the wet
etch. Unfortunately, both of these features were left unprotected by photoresist in the
mask design and hence experienced a partial undercut during the isotropic wet etch.
Fortunately, some of the alignment marks and ridges survived, but not enough for a
quality process. Figure 23 illustrates some of the features that were affected by the metal
adhesion problem.
Initially it was thought that annealing the contacts might promote adhesion to the
surface. Annealing causes the metal and semiconductor to intermix forming new
compounds, which might promote adhesion. A 30 second rapid thermal anneal at 400*C
was performed before the wet-etch. This had little to no affect on the adhesion, but an
anneal was performed on all subsequent wafers to be safe. After annealing, the metal
surface became noticeably bumpy. Surface roughness due to annealing is expected and is
61
a motivation for using non-alloyed contacts [45]. However, no straightforward nonalloyed contact could be found in the literature [45]. Also, Au containing contacts are
known to exhibit a poor surface morphology [47]. To verify that the metal was not being
etched, the ohmic contact metal was evaporated on a bare silicon wafer and dipped for a
total of one minute in a 1:1:20 H2 SO 4 :H 2 0 2 :H 20 solution. No measurable etching of the
metal occurred.
A.)
B.)
Metal unattached
Pieces missing from Verniers
C.)
Stripe is gone
Figure 23: Examples of metal adhesion problems after wet-etch. A) Rows of stripe lasers with an
integrated loss-section. Metal is only attached to the large contacts which were protected by photoresist. B)
Vernier alignment marks have missing pieces. C) Three rows of stripe lasers with the 3 rd row completely
missing.
A scanning electron micrograph of the contact metal on a ridge of one of the
lasers that was formed by wet-etching is shown in Figure 24. Immediately noticeable is
the sloped, rough sidewalls of the ridge, and the uneven surface of the metal. Wet etches
should yield smooth surfaces, but the semiconductor ridge is rough. Considering the
magnification of the images, the sidewall roughness is estimated to be about 50nm, which
is about 3% of the smallest stripe width. After annealing, the metal sidewalls might have
roughened by a small amount. This roughness would then transfer into the underlying
ridge. Consequently, an anneal should not be performed before the wet-etch although
detailed studies were not carried out to confirm this hypothesis.
62
Figure 24: Annealed metal contact that was used to fabricate the self-aligned ridge waveguide. The lack of
surface morphology is probably due to the contact anneal.
The features in Figure 24 also suggest one possible explanation for the metal
adhesion problem. The undercutting process leaves about 0.2pm of overhanging metal on
each side of the ridge. Since the smallest features are 1.5pm in width, there may not be
enough material for the metal to adhere to after the etch. Another possibility is that a
surface oxide develops on the GaAs before the metal is evaporated. A suitable process
would then require a HF dip immediately prior to depositing the metal. One final
possibility is that Au-based contacts simply do not adhere well to GaAs.
There are several options to alleviate the problems associated with the exposed
metal during the wet-etching of the arsenide-based material. An immediate solution is to
dry etch the wafers rather than wet-etch the wafers. Because a suitable dry-etch process
can take a long time to develop, it was not attempted in this work, but once a process is
developed, dry etching can be very effective. Since dry etching produces vertical
sidewalls, there will be no overhanging metal. If indeed, the large amount of overhanging
metal is the cause of the adhesion problem, dry etching would be an excellent solution,
assuming the contact metal is also a good hard mask. Another option is to use a SiO 2 (or
SiNx) hard mask instead of the metal. This would entail the deposition of SiO 2 before step
63
1. Positive resist, rather than negative resist, would be patterned using the original metal
mask, followed by etching the SiO 2 . The SiO 2 hard mask would not be removed until the
GaAs-based material is etched, after which the original p-type contacts are re-patterned
onto the wafer using steps one and two [Figure 25]. This method does require good
alignment during the re-deposition of the metal, but it avoids dry etching. Figure 25
illustrates how the ridge of a stripe laser would be formed using this method.
Pattern Mask I
into +Resist
etch S102
Deposit SiO.
Pattern Mask I Into -Resist
Evaporate metal
ADDIy resist Pattern
Mask 2 and etch
arsenide remove
iO
Lift-Off
Figure 25: Cross-sectional schematics of an alternative method to form the ridge of the stripe laser without
using metal as a wet-etch mask. This method does not require any dry-etching, but does require good
alignment during the re-patterning of Mask 1. It is important to realize that one must apply and pattern
Mask 2 before wet-etching the GaAs-based material in order to form the p-type beam of the photonic
crystal lasers. Plus and minus signs in front of resist indicate positive or negative resist respectively.
Yet another option is to modify the existing mask set so that all of the metal
features are protected by photoresist during the wet-etch. This entails a simple re-design
of the base alignment marks and the integrated stripe lasers in mask 2. Of the three
options so far, this would probably require the smallest amount of time, because no labrelated development is necessary.
64
Finally, one can simply continue the process as is, since there are a fair amount of
stripe lasers and base alignment marks remaining on the wafer after the wet-etch.
Unfortunately the stripe lasers with 1.5pm wide ridges usually do not survive the wet
etch, but the stripe lasers with the wider ridges can still be used to test the material.
Fortunately, a second set of electron-beam lithography alignment marks are formed
during the patterning of the n-type ohmic contact metal [Figure 26], so that good
alignment can still occur for each electron-beam field even in the worst case scenario
where all of the base alignment marks no longer exist. Special care was taken in the mask
design to protect the electron-beam lithography alignment marks during all subsequent
steps. For negative photolithography processes, the alignment marks are already
protected, but for the positive processes, a box was placed around the electron-beam
lithography alignment marks to protect them from being etched. The use of a "cross
within boxes" alignment marks makes it easy to obtain accurate alignments because the
electron-beam written features do not cover the alignment marks. This is not the case for
the global alignment marks that were created using mask 1. Thus, the electron-beam
lithography alignment marks are recommended for any future mask designs.
Metal Alignment Mark
Box feature to
protect metal
E-beam pattern
Figure 26: Electron-beam field alignment marks included in the mask design that were formed during
second metal deposition.
65
4.2.4. Steps 4-5: Formation of ohmic contacts to n-type phosphide-based
material
The most popular ohmic contact to n-type phosphide-based layers is AuGe/Ni/Au
[51], but the AuGe alloy is not available in NSL. Therefore, a Au/Ge/Au contact, with a
contact resistivity of approximately 10-7 0cm 2 was used [52]. The process used to form
the n-type contacts is identical to steps 1-2 except that Au(400A)/Ge(200A)/Au(1600A)
was evaporated using electron-beam evaporation. Again, the photolithography and lift-off
processes were very consistent resulting in well defined small features, such as the
aforementioned electron-beam lithography alignment marks.
Figure 27: Unit Cell after steps 4-5. Compare to Figure 15(c).
4.3. Remaining Fabrication Steps: Discussion
Work on the photonic crystal laser was suspended after the second contact
deposition. Consequently, some difficult fabrication steps still remain. Fortunately, past
members of the Integrated Photonics Devices and Materials group have already
undertaken many of these remaining processing steps. The aim of the following sections
is to give suggestions on the remaining processing steps using the lessons already learned
by these previous members, and to present the results from initial processing experiments
that were performed as part of this thesis.
66
4.3.1. Steps 7-10: Dry etch of InP and GaAs materials. Patterning of
SiO 2 hard mask
Steps 7-10 are only necessary to fabricate the stripe laser, or if Focused Ion Beam
etching is used, to create the sub-micron features of the microcavity lasers. Since the
stripe laser is only a diagnostic device, these steps can be skipped without affecting the
fabrication of the photonic crystal laser as long as electon-beam lithography is used to
pattern the sub-micron features. However, many of the processes that are used in
fabricating the photonic crystal laser also occur in steps 7-10. Hence, not only will the
stripe laser help verify the quality of the III-V material; its fabrication will also serve as
an initial test of the forthcoming fabrication processes.
The SiO 2 is typically used as a hard mask for the plasma etching of both
phosphide and arsenide-based semiconductors. SiO 2 is first deposited using plasmaenhanced chemical vapor deposition (PECVD) and the wafers are then coated with
positive photoresist. The photoresist is patterned, and the SiO 2 is then etched using
reactive ion etching.
Indium containing material such as InP is typically etched with a combination of
methane and hydrogen (CH 4/H2 ), while GaAs is typically etched in a chlorine-based
plasma such as a BCl 3 plasma. At the time of this work, hydrogen/methane etches were
no longer available in NSL due to cross-contamination issues with other etches; a new
dedicated hydrogen/methane etcher was being constructed elsewhere in the laboratory. A
hydrogen/methane etch is available in the TRL PlasmaQuest etcher, but previous work
[43] has shown that polymer formation during hydrogen/methane etching causes
significant problems with subsequent etches. Specifically, a polymer coats the chamber
and sample acting as an etch mask during subsequent etches. To remove the polymer a
67
series of chamber cleans and sacrificial etches must be performed. Cleaning the
PlasmaQuest etcher requires a TRL staff person to disassemble and mechanically clean
the chamber. One can also try different InP etch chemistries as in [53]. The use of a
heavy, inert atom such as argon during the GaAs etch has been found to produce mirror
smooth sidewalls [54].
Since photoresist can not withstand neither a BCl 3 etch or a hydrogen/methane
etch, Si0 2 is used as a hard mask. To pattern the Si0 2 , either photoresist or a metal such
as nickel can be used as an etch mask. Initial work, using AZ5214 as a positive resist,
showed that CF 4 should be used to dry etch the Si0 2 , rather than the more common
CF 4 /0 2 combination, as the reactive 02 in the plasma etches the photoresist. A two
minute, 120'C hot plate post-bake of the AZ5214 photoresist also improved the ability of
the photoresist to withstand the dry etching process. References [55-56] showed that a
flood exposure of the resist, an optimized post-bake, a low DC bias, and a thin layer of
SiNx helped to obtain SiO 2 sidewall variations to less than 500A. The use of SF was also
recommended over CF 4 for the etch chemistry. Since 500A variations were observed for
wet-etching arsenide-based semiconductor material (section 4.2.3), these methods should
yield etch roughness comparable to wet-etching, but with vertical sidewalls.
4.3.2. Steps 11-12: Electron-beam lithography or Focused Ion Beam
etching for photonic crystal active region
Two options, Focused Ion Beam etching (FIB), or electron beam lithography and
subsequent etching are capable of patterning of the submicron features required for the
active region of the microcavity laser. Focused ion beam etching requires no hard mask,
68
I
because features are directly written and etched with an ion beam making FIB an ideal
choice. Initial contacts were made with Mr. Richard San Martin of FIB-X Corporation.
In electron-beam lithography, features are written into photoresist, implying that a
hard mask such as SiO 2 is required and ensuing dry etches must be utilized. Specialized
resists are required for the high resolution electron beam lithography process. Previous
work [43] showed that hydrogen silsesquioxane (HSQ) can be used as a resist but can not
be used as a hard mask, although the use of a thin layer of Si0 2 might alleviate the
problems with HSQ. If HSQ is not used, a multi-step process using Poly(methyl
methacrylate) (PMMA) resist has already been designed [43]. The top view of the
process steps leading up to etching of the submicron features is shown in Figure 28.
At this point in the process either pieces of the wafer or full wafers can be
fabricated. The mask set was designed with fairly stringent tolerances on all alignments.
To guarantee operation, the masks can not be misaligned by more than 0.5pm during
each exposure step.
Pattern PMMA with e-beam
Evaporate and lift-off Ni
Apply and
pattern resist
Etch SiO, remove Ni
Figure 28: Electron-beam lithography process leading up to the etching of the submicron features. Some
layer colors are made partially transparent to reflect actual visibility.
4.3.3. Steps 13-14: Undercut removal of Phosphide-based material
Undercutting, or the sacrificial etching of AlGaAs was thoroughly studied
previously [50], in which GaAs features as long as 15pm were suspended in air. Since the
69
phosphide-based material is the material to be etched in this work, a different wet etch
chemistry such as H3PO 4 :HCl (3:1) [49] will be required.
4.3.4. Step 15: Etching of SiO 2 to open up contact vias
The SiO 2 above the metal contacts is removed using negative photoresist as an
etch mask. Although the complete removal of SiO 2 will enhance the index contrast of the
entire structure, the SiO 2 etching process might cause etching damage to the active area or
to the output waveguide. Therefore, SiO 2 is only removed from the metal contact pads to
allow contact with a current probe.
4.3.5. Step 16: Thermal oxidation of AlAs
The oxidation process is critical to the photonic crystal laser design. Without the
oxidation process, a parasitic p-n junction via the substrate exists in parallel to the
microcavity lasers. Also, the output waveguide would rest atop a relatively high index
cladding causing light to couple to the substrate. To ensure electrical isolation between
the contacts, the width of the p-type contact pads are less than 11 Om, allowing the AlAs
underneath the pads to be fully oxidized while still allowing the pads to be sufficiently
large for easy alignment to a current probe. Large scale oxidation of AlAs has been
successfully demonstrated and studied by numerous researchers in the Integrated
Photonic Materials and Devices Group.
4.4. Fabrication of a generic ridge laser
In order to test the quality of MBE-grown material, ridge lasers were fabricated
with similar materials to those of the photonic crystal laser. Unlike the diagnostic stripe
laser device described in Chapter 3, the ridge lasers were fabricated on different samples
70
than the photonic crystal laser. The ridge lasers also differ in how current is injected into
the device. In the ridge lasers, current is injected from above through a top-side metal
contact and from below, through bottom-side metal contact. Thus, current flows through
the substrate and the lower AlAs layer. Consequently, the AlAs layer must be doped and
cannot be oxidized, so that a low-resistivity current path exists from the bottom-side
metal to the active region. A schematic of the ridge laser is shown in Figure 29 along
with a fabrication sequence.
Top~ewe M"ta
3502
02
Sottom-.i
1: Pattern resist
2: Etch
3: Deposit Oxide
Metal
4: Pattern Resist
and etch
5:Pattern
Resist
6: Aoglv Metal
Lift-off
7: Thin Wafer
Apply n-metal
Figure 29: The ridge laser with accompanying fabrication sequence.
A process flow, employing self-aligned ohmic contacts, was also utilized, but the
same metal-liftoff problems were observed. Also, the self-aligned contacts completely
peeled off during the PECVD SiO 2 deposition.
Two sets of test wafers were grown specifically for the ridge laser. Sample VA36
was exactly like the quantum well sample, VA34, except that the lower AlAs layer was
doped so that a bottom-side contact can be used. Sample VA37 was an experimental
wafer containing 4 DWELL active regions and a digital alloy for the output waveguide.
71
The quantum dot wafer, sample VA37, emits at 1250nm but its emission width is quite
broad in comparison to the photoluminescence from the strained quantum well wafer,
sample VA36 as shown in Figure 30.
72
VA37
10nm p-GaAs: Be
125nm p-Al 4,Ga 5,As: Be
35nm GaAs
5nm GaAs
6nm In.1 Ga8,,As
.85nm InAs
2nm In,,Ga85As
VA36
10nm GaAs: Be
125nm AI.49Ga.51As: Be
15nm GaAs
8nm In.15Ga.85As
15nm GaAs
X4
10nm GaAs HighT
5nm p-GaAs:Be HighT
20nm GaAs HighT
5nm GaAs
8nm In.15Ga.85As
25nm AI4,Ga.5 ,As
15nm GaAs
25nm AI.49Ga.51As
400nm n-In 53Ga 47P: Si
19nm n- n.sPGa.P:
Si
4
Inm n-GaAs: Si
n-In19
3Ga47P: S
500nm AlAs: Si
}
X19
X9nm
500nm n-AlAs: Si
GaAs: Si Buffer
GaAs Substrate
GaAs: Si Buffer
Grown Structure PL
8
7
65
-
4
4-
-
C
VA36
VA37
3-
0
60
750
850
950
1050
1150
1250
1350
1450
-1 Wavelength
Figure 30: Grown structures and measured PL data.
73
The photonic crystal lasers and generic ridge lasers were fabricated in parallel up
to process step number 6 of the photonic crystal laser process flow. Unfortunately, the
metal adhesion problems were not discovered until both sets of wafers were processed.
Thus, the only wafer that went through the desired process flow was sample VA36 wafer
number two. Due to damage to the lapping equipment, the wafers could not be lapped,
thus a final step still remains to be completed before the lasers can be tested. Figure 31
shows sample VA36 before the top metal was evaporated.
Figure 31: Sample VA36 before the second contact deposition. Stripes widths are as small as 1.5pm
As a comparison to the photonic crystal microcavity laser, the same rate equation
analysis was employed to predict the L-I curves for the ridge laser. As shown in Figure
32, the sharp transition in the emitted power at threshold, which does not occur for
microcavity lasers, does occur for the ridge lasers. As previously mentioned, microcavity
lasers generate a large proportion of photons into the lasing mode before the onset of
stimulated emission, thus the microcavity photonic crystal appears thresholdless on an LI curve.
74
Power vs. Injection Current
3
x 10
2.5 --
2-
S1.5
0.5
0,
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
Injection Current (A)
Figure 32: L-I curves for a ridge laser
75
Chapter 5.
Conclusion and Future Research
5.1.
Further Investigations
5.1.1. Improvement to the rate equations
The rate equation analysis presented in Chapter 3, and elaborated on in Appendix
2, contained many assumptions. In particular, the proportion of photons exiting the output
mirror was assumed to be % meaning the two mirrors of the Fabry-Perot laser cavity
were assumed to have equal reflectivity. This assumption simplified the rate equations by
avoiding the details of how the light intensity as a function of space varies with the
reflectivity of the mirrors. A more accurate model utilizing the laser rate equations is
found by decomposing the resonant mode into counter-propagating waves [57]. The
probability distribution of the photon density for each wave can be found from [32],
dN
2
1 V
/ j, BN -<a>Np
dz
2V
(10)
where Np" is the photon density traveling in either the plus, or minus, z-direction. The 1/
=
g-
P
..
factor in front of the lasing mode spontaneous emission rate accounts for the equal
chance of photons being spontaneously emitted into each of the counter-propagating
waves. The above equation can be solved using a finite-difference technique already
developed for Semiconductor Optical Amplifiers [30], in combination with the carrier
density equation already introduced in Chapter 3. The boundary conditions at the mirrors
76
(figure 33) can then be applied to determine both the solution to N(z), and the output
power.
R1
NNN+=
R2
R1N-
Z=0
(1 -R2),
N +
Z=L
Figure 33: Boundary conditions for an optical cavity.
5.1.2. Testing of the Photonic Crystal Microcavity Laser
In Chapter 3, the output power of the microcavity laser was predicted to be on the
order of microwatts. A small output power, in conjunction with coupling and propagation
losses associated with the output waveguide, will make it difficult to detect the output
light. One way to confirm the successful lasing of the device is to observe light exiting
the top of the laser. Light exiting the top of the laser does not fulfill the total internal
reflection condition because it was either scattered or is the result of spontaneous
emission into a non-resonant mode. Thus, one would observe a noisy output from the top
of the laser. However, once threshold is reached, a majority of the light in the cavity is
the result of stimulated emission into the lasing mode. Undoubtedly some of the lasing
mode photons will scatter and exit the laser vertically, so one can still observe line-width
narrowing from this vertical output. In fact, many of the lasers presented in Chapter 2
were the result of light exiting the cavity vertically through so-called leaky modes. To
ensure enough light leaks out of the top, one must pattern extra holes in the bottom
77
waveguide to increase the reflectivity of the photonic crystal mirrors. This method will
confirm successful lasing, while eliminating the complication of coupling and
propagation losses.
5.1.3. A laser incorporating adiabatic tapers
Because the gain medium resides above the output waveguide, there is a trade-off
between the modal gain and the laser output power. To minimize this tradeoff, an
alternative design is proposed and is shown in Figure 34. The design employs adiabatic
tapers to gradually vary the effective index as light approaches the output waveguide
from the cavity. By gradually removing material from the top surface, the optical mode
couples into the bottom waveguide with a minimum of loss. This design does require a
different mask set along with greater fabrication precision to form the tapers. Therefore,
it should only be attempted after the original laser design is successfully demonstrated.
Figure 34: Top view of a photonic crystal laser utilizing adiabatic tapers
5.1.4. A microcavity laser with mirror confinement in three directions
The modes of an optical resonator can be broadly separated into three categories.
5 The alternative
design was suggested by Dr. Gale Petrich
78
1.) Modes, which satisfy the boundary conditions of a resonator and are totally
internally reflected at all interfaces, are referred to as resonant modes. The
lasing mode of a resonator is classified as a resonant mode.
2.) Modes, which do not satisfy the boundary conditions of their environment and
can not exist, are called evanescent. These modes carry no time average power
[58], and hence, by conservation of energy, an atom can not emit a photon
into one of these modes. The effect of a cavity is to add more restrictions on
the boundary conditions, so that more modes are evanescent.
3). Modes, which satisfy all the boundary conditions of the resonator yet are not
totally internally reflected at one or some of the interfaces, are commonly
referred to as leaky or radiation modes. Reflectors such as photonic crystals or
gold mirrors can be used to reflect light of certain frequencies forcing the light
to be totally internally reflected and thus eliminate many of the radiation
modes. In eliminating radiation modes, these reflectors eliminate vacuum
modes which can induce a medium to spontaneously emit photons into these
lossy modes. It would thus be advantageous to create a microcavity laser
confined by perfect mirrors in all directions, so that radiation modes can be
suppressed.
One example of such a microcavity is the spherical Bragg resonator, a "Bragg
onion resonator" [59], but it is unclear how a gain medium can be incorporated into the
structure. A new laser structure that is capable of trapping light with mirrors in almost all
directions is proposed and is schematically shown in Figure 35. Both of the proposed
structures utilize a two-dimensional photonic crystal slab to confine light laterally. The
light is coupled into a photonic crystal waveguide and exits the laser in the plane of the
chip. Both proposed structures also utilize Bragg reflectors to confine light vertically and
to isolate the light from the substrate. The Bragg reflectors can be partially oxidized
similar to an oxide confined vertical cavity surface emitting laser (VCSEL), so that a
higher index contrast exists in the photonic crystal slab. The lateral oxidation front must
be precisely controlled in order to construct a conductive path from the bottom-side
contact to the active region. The structure in Figure 35a. incorporates Bragg gratings
vertically around the active region to confine the light in the vertical direction. In Figure
79
35b, a conducting low index dielectric, indium tin oxide (ITO) is placed above the active
region. The ITO confines light by index confinement, and the top-contact also acts as a
mirror to reflect any light which propagates vertically through the ITO. The incorporation
of ITO allows for a layered structure that would be simpler to integrate with other optical
components.
A.)
r--0Via
4
S'0
2
* GaAs
-
Bragg Layers
AIGaAs/AIAs
Metal
B.)
SVia
Si0 2
Indium Tin Oxide
Gain
GaAs
Fig r
: 2v
s of a 3D m
r c
Bragg Layers
d mAcGaAs/A As
Figure 35: 2 variations of a 3D mnirror confined microcavit aser
80
__N
Each of these lasers provide quasi three-dimensional confinement meaning that
spontaneously emitted light is less likely to couple into radiation modes. Mirror
confinement is desired over index-guided structures, because index-guided structures
allow a near continuum of vacuum modes to be present in the laser oscillator. This is due
to the nature of index confinement, which operates on the principle that light approaching
an interface at an angle greater than the critical angle will not be totally internally
reflected. Thus, there is a finite cone of modes in k-space which are not totally internally
reflected (sometimes referred to as an extraction cone), and can thus be characterized as
radiation modes. Consequently, mirror-guided structures will drastically increase the
spontaneous emission factor. Additionally, the proposed laser is edge emitting and is
electrically activated making such a laser suitable choice for integrated optics.
5.2. Final Conclusions
The field of microcavity research is now widespread, and microcavities are just
beginning to find permanent applications. A microcavity laser has recently been applied
to the field of biomedicine, where it is used to detect tumor cells during surgery [60].
When combined with special filters, the refractive index change in microcavities can also
be used to detect various chemical agents. Low-loss microcavities operating in the strong
coupling regime are a viable source for quantum computation. Microcavity lasers have
been theoretically and experimentally proven to outperform larger lasers in all categories
with the exception of high output power. However, the lack of an electrically-activated,
edge-emitting, microcavity laser has made it difficult for microcavity lasers to penetrate
the field of integrated optics.
81
This thesis has presented the physics, design, and initial fabrication of a
microcavity laser that is an excellent candidate as a light source for use in integrated
optics. Using the phenomenon of vacuum fields, cavity quantum electrodynamics has
been explained to provide a physical picture of spontaneous emission in a microcavity. A
hybrid fabrication approach has been presented that should simplify the device
processing. Problems with metal adhesion to p-type GaAs were encountered during
fabrication, and various solutions to these problems have been suggested. The remaining
fabrication steps have all been performed within the Integrated Photonic Materials and
Device group. Suggestions from past members have been compiled to aid one in the
remaining processing steps. The optical masks have been designed to ease testing, so that
one can quickly qualify the optimal variation of the laser. When completed, the photonic
crystal microcavity laser will represent a major improvement in edge emitting lasers.
Finally, new microcavity lasers have also been proposed that could also find a niche in
the field of integrated optics.
82
Appendix 1: Index of refraction for AlGaAsl-x
%*Function calculates the refractive index of AlxGa_1-x. User inputs x and
%the wavelength in meters
%All formulas and functions taken from Chuang "Physics of Optoelectronics
%Devices, 1995. pp. 249.
h=6.63e-34; %Planks constant
h_bar=h/(2*pi);
c=3e+8; %speed of light
c_cm=3e10; %Speed of light in centimeters.
h_cm=4.14e-15;
%Plank constant in microelectronic untis.
hbarcm=hcm/(2*pi);
kt=.0259;
%Thermal voltage in eV
epsilonO=8.85e-12; %Value in meters
epsilonGaAs=13*epsilonO;
q=1.6e-19;
%The permittivity of GaAs
%Charge of electron
lambda=1.3e-6; %INPUT WAVELENGTH IN METERS
w=c*2*pi/lambda;
Ep=h*c/(q*lambda); %Photon energy in eV
x=.48; %INPUT PROPORTION OF ALUMINUM
Eg=1.424+1.266*x+.26*(x)^2; %Bandgap of AIGaAs in eV
delta=.34-.5*x;
A=6.64+16.92*x;
B=9.2-9.22*x;
yso=Ep/(Eg+delta);
y=Ep/Eg;
fy=1/y^2*(2-(1+y)^.5-(1-y)^.5);
fyso=1/ysoA2*(2-(1+yso)A.5-(1-yso)A.5);
EpsilonFactor=(A*(fy+.5*(Eg/(Eg+delta))A(1 .5)*fyso))+B;
n_AIGaAs=EpsilonFactorA.5
83
Appendix 2: The Phenomenological Rate Equations
The carrier rate equation can be written as,
v Eg
I
dN
CN 3 - BN 2 - AdN - As1rf N - vEu-atgio
dd t
17q V -9V
3
P
E quation A I
3
where N is the free carrier density in the active region (cm- ), and Np is the lasing mode
photon density in the laser cavity (cm-3).
I
" q -- is the generation rate of carriers in the active region due to pumping.
qV
Thermal generation of carriers does not have to be accounted for, because it is
cancelled by the thermal equilibrium recombination rate. I is the terminal
current (Amps), while V is the volume of the active material (cm 3). qi is the
injection efficiency - the fraction of carriers actually injected into the active
medium. Carriers can be lost before reaching the active material through
recombination, or they can leak out of the non-infinite quantum well after
being injected.
" CN 3 is the carrier loss rate due to Auger recombination. Since Auger
recombination requires three carriers, the rate is proportional to N 3 for
intrinsic active materials. C is the Auger recombination coefficient (cm 6 /s).
" BN is the loss rate of carriers through spontaneous emission into all modes,
RS. Since spontaneous emission requires a free electron and a free hole, the
recombination rate is proportional to the NP product, but charge neutrality in
the undoped active material demands N=P. The square law actually only holds
in the Boltzmann limit, but it is very common to assume that it holds for larger
carrier densities. The factor B is the biomolecular recombination coefficient
_
v
(cm 3/s). In reality, this factor is affected by the cavity surrounding the gain
"
"
*
medium and is not a strict material parameter. However, the net
recombination rate is assumed to be a material parameter in this thesis, with
only the coupling to the lasing mode being affected by the cavity.
AdN is the carrier loss rate due to defects. In this thesis, high quality active
material is assumed so that Ad can be set to zero.
AsurN is the carrier loss rate due to surface recombination in the active region.
The surface recombination coefficient, Asu,. is given b, Asu=vsas/V where as
is the exposed surface area of the active region (cm) and v, is the surface
recombination velocity (cm/s). The term vsN is simply the flux of carriers at
the surface and as/V simply spreads out the flux over the gain region. The
surface recombination velocity is much larger for exposed surfaces than for
the surfaces between epilayers, so the surface area is given by as=2T(L+W)
where T,L and W are thickness, length and width of the active material
respectively.
The term, vg
L']gN, is the stimulated emission rate into the lasing mode. It
is noted that stimulated emission can occur into other modes, but high spectral
purity is naturally assumed in this laser so that stimulated emission into the
84
lasing mode is dominant. The gain, g (cm-) is empirically modeled as,
g=goln(N/Na,) where go is the large signal gain and N,. is the transparency
carrier density. F is the confinement factor which in most practical cases is
simply the photon energy in the gain region divided by the photon energy in
the entire cavity for the lasing mode. Often, Pg is referred to as the modal
gain. The term, VJ/V where V is the cavity volume (cm 3), is a weighting factor
accounting for the difference in volume between the gain region and optical
cavity. Finally, since material gain is defined in terms of length, multiplication
by the group velocity, vg (cm/s) converts the gain to a per unit time basis. The
group velocity is given as cineff where neff is the effective index which was
calculated from the Optiwave simulations.
The photon rate equation is written,
dN
V
= vggNp+ -/spB
d it
P
N2
V
_
g
<a>
N
Equation A 2
* The spontaneous emission rate into the lasing mode, R p is given as, 3pSBN 2
where sp,is the spontaneous emission factor, which can be understood as
R sp/Rs,. Where Rsp=BN2 is the net spontaneous emission rate. The
confinement factor for the lasing mode, F, is actually buried in the
spontaneous emission factor, as spontaneous emission into the lasing mode is
impossible for F=O. The term, V/V in front of the spontaneous emission factor
accounts for the difference in volume between the gain medium and optical
cavity.
* vg<a>N is the photon loss rate where <a>is the modal loss (cm'). The modal
loss can be broken up into the external loss due to mirrors <am> and the modal
loss due to internal loss processes, <ai>. By assuming a Fabry Perot cavity,
1
1
) where R, and R2 are the power
the mirror loss is, <am>= - ln(
L
RR 2
reflection coefficients of the two mirrors and L is the axial length of the cavity.
This equation explicitly shows how shorter cavities experience a greater
mirror loss rate. The photonic crystal reflectors can actually introduce a phase
shift to the oscillating field [61] so in reality the effective length of the cavity
must be altered to maintain real reflection coefficients [61]. However, this
effect was ignored in the calculations. The internal modal loss can further be
written as the loss due to free carrier absorption, scattering, and traps. Photon
loss due to direct band absorption is accounted for in the material gain which
is negative if the material is absorbing.
Setting Equation Al equal to zero and solving for the photon density gives,
85
Tp
Ns
B
1g< a> -itg
g
Equation A 3
One can then set the carrier rate equation equal to zero and substitute the above
value for Np into it. The resulting equation is,
1
0 = 7i q
- CN - BN2 - AdNC
As11,fN-
11gT g/pBN2
9
vg< a> -igTg Equation A4
Thus, a single equation is obtained where the only unknowns are the injection
current rqJ, and the carrier density, N. This equation is solved by plugging in a value for I,
and then calculating the value of N that produces a result equal to zero. The function
fzero in Matlab is used. Before threshold, the initial guess value for fzero is simply the
previous value. After threshold, the guess is modified to be just smaller than the
asymptotic value that N approaches. This is necessary because Matlab falsely interprets
singularities as intercepts. To find this asymptotic value one simply sets the loss equal to
the gain. Assuming a logarithmic gain model, the resulting equality is,
<a>
= Tgln
(N N)
Nt r
Equation A 5
Solving for N in the equation above yields the asymptotic value that the carrier
density approaches. It is noted that this method is slightly different than the more
common method of simply assuming a logarithmic carrier density and plugging a predefined carrier density into the rate equations. In the method presented here, the carrier
density as a function of current naturally results from the rate equations.
86
in
Input
A
L,
W
tp
t
twg
neff
R
Description
wavelength of lasing light
Axial cavity length
Horizontal Cavity Width
Vertical cavity thickness
Active material vertical Thickness
Output waveguide thickness
Effective Index of cavity mode
Power Reflectivities
Value Used
9.60E+02
0.6
0.6
0.675
0.01
0.4
1.819
0.99
4.00E-29
7.OOE-1 1
1.50E+05
Units
nm
pm
pm
pm
pm
pm
cm /s
cm3 /s
vs
Auger Recombination Coefficient
Biomolecular recomb coefficient
Surface recomb velocity
Ntr
Transparency carrier density
1.80E+18
cm's
go
a(GaAs)
a(InGaP)
Large signal gain
total loss coefficient for GaAs
total loss coefficient for InGaP
2.1OE+03
2.85E+01
8.OOE+00
cm
dB
dB
C
B
cm/s
Table 2: List of values used in rate equation program
Following is the Matlab code used to simulate the rate equations.
%Code simulates the rate equations
warning off MATLAB:fzero:UndeterminedSyntax
%Fundamental Constants used in the code
h=6.63e-34; %Planks constant
h_bar-h/(2*pi);
c=3e+8; %speed of light
c cm=3e+8*100;%speed of light in centimeters/s
h_cm=4.14e-15; %Plank constant in microelectronic untis.
hbarcm=h_cm/(2*pi);
%Global Variables declared for use in a seperate function
global V;
global C auger;
global B;
global Asurf;
global Vp;
global Gamma;
global vg;
global go;
87
global Ntr;
global Bsp;
global alpha;
global Gammam;
global alpham;
%Free space assumed Wavelength in m.
lambda=960e-9;
lambdacm=lambda* 100; %Wavelength in cm
%angular frequency in rad/sec is independant of material for
w=c*2*pi/lambda;
semiconductors
%frequency in hertz independant of material your are in.
f=c/lambda;
%Length of active material volume and cavity volume in cm.
Lz=.6e-4;
%width of active material volume and cavity volume
W=.6e-4;
%thickness of active material volume
t=.01e-4;
%thickness of the photon cavity volume
tp=.675e-4;
%thickness of output wg and thus mirror height
twg=.4e-4;
%Effective Index found from Optiwave simulations.
neff=1.819;
%Power reflection coefficient of PC mirrors
R=.99;
%Auger coefficient for InGaAs GaAs QWELLs
C_auger-4e-29;
%Biomolecular recombination coefficient for QWeLLs
B=.7e-10;
%Surface recombination velocity in bulk InGaAs p.151 of C&C
vs=1.5e5;
%surface area of active material
as=2*t*(Lz+W);
%volume of active material
V=t*Lz*W;
%photon cavity volume
Vp=tp*Lz*W;
%Surface recombination coefficient
A_surf=asN*vs;
%group velocity in cm/s
vg=ccm/neff;
%Transparency carrier density
Ntr--l.8e+18;
signal gain
%Large
go=2 100;
alphadBFreeCarrier-4; %Free carrier loss coefficient in N-InP in dB.
%Trap loss coefficient for InP in dB
alphadBTrap= 1;
alphadBScattering=3; %Loss coefficient in InP due to scattering in dB. Could be more
due to small width
alphadBInP=alphadBFreeCarrier+alphadBTrap+alphadBScattering %Total internal loss
coefficient for InP in dB
alphadBFreeCarrierGaAs=22; %Free carrier loss coefficient for GaAs
alphadBTrapGaAs=3.5; %Loss in GaAs due to deep traps
alphadBScatteringdB=3; %Scattering loss for GaAs
alphadBGaAs=alphadBFreeCarrierGaAs+alphadBTrapGaAs+alphadBScatteringdB
%Total loss coefficient for GaAs
alphadB=twg/tp*alphadBInP+(tp-twg)/tp*alphadBGaAs; %Weighted average of loss in
each material system.
%gives modal loss. In reality could use
%confinement factor for
%each matarial
alpha= 10^(alphadB/20) %Value of loss coefficient in cm^- 1
88
%Confinement factor for evenly distributed photon density
Gamma=V/Vp;
%output mirror confinement factor
Gamma_m=twg/tp;
alpham=1/Lz*log(1/R); %mirror loss coefficient
loss=vg*alpha+vg*Gamma_m*alpham; %The loss per unit time felt by mode
%The asymptotic value that N
N_asymptote=Ntr*exp(loss/(Gamma*vg*go));
approaches is value when gain=loss
for Spontlndex=1:1:6,
Bsp=(SpontIndex-1)*9e-3+.005; %vary spontaneous emission factor from .005 to .05
with 6 data points
%Initial Guess for the carrier density at the lowest current input. A
Nguess=Ie18;
value between
%1e16 and Ie19 always works. This usually needs to be
%adjusted if parameters change though. Otherwise Matlab
%gives an error.
ThresholdFlag=O; %Initialize flag for reaching threshold to off
%Factor just to keep track of injection current
m=0;
index=0;
%Keeps track of increments in current. This should be adjusted in
delta= 1 e-6;
%different situations
for m=1:1 1e3,
index=index+1;
I=m*delta;
Nfind=fzero('Rate',Nguess,[],I);
Np(index)=V/Vp*Bsp*B*Nfind^2/(vg*(alpha+Gammam*alphamGamma*go*log(Nfind/Ntr)));
Rst(index)=Vp/V*Gamma*vg*go*log(Nfind/Ntr)*Gamma*Bsp*B*Nfind^2/(vg*(alpha+
Gammam*alpham-Gamma*go*log(Nfind/Ntr)));
%Stimulated emission rate is plotted for fun.
Rsp(index)=Vp/V*Gamma*B*Nfind^2; %Spontaneous emission rate is plotted
gain=Gamma*vg*go*log(Nfind/Ntr); %Value of gain for the given input current
%Net gain is plotted for fun.
netgain(index)=gain-loss;
Pout=.5 *vg*alpham*Np(index)*Vp*h*f; %Value for output power
Yaxis(index)=Pout;
Xaxis(index)=I;
Yaxis2(index)=Nfind;
%Only perform the following when haven't reached
if ThresholdFlag==0
%threshold yet
%Ifhaven't reached threshold, make the guess in fzero
Nguess=Nfind;
%adaptable by setting equal to current value
if Np(index)*Vp>1 %Ifhaven't reached threshold, When have a total of 1
%photon in cavity then have reached threshold.
ThresholdCurrent=I %Print the threshold current to screen
N_threshold=Nfind %Keep the current threshold carrier value
89
ThresholdFlag=1; %Let program know threshold has been reached
%end checking to see if one total photon in cavity.
end
%Case when ThresholdFlag=1, when already reached threshold.
else
Nguess=N_asymptote-1e14; %if reached threshold set the guess in fzero equal to
%the value N approached asymptotically
%Must do this because fzero chooses the wrong value causing
%gain>loss which is unphysical.
%End checking to see if have reached threshold
end
%End for loop containig injection current
end
%Keep the current graph on the axis to overlay graphs
hold on;
switch SpontIndex
case 1,
loglog(Xaxis,Yaxis,'k')
case 2,
loglog(Xaxis,Yaxis,'k')
case 3,
loglog(Xaxis,Yaxis,'k')
case 4,
loglog(Xaxis,Yaxis,'k')
case 5,
loglog(Xaxis,Yaxis,'k')
case 6,
loglog(Xaxis,Yaxis,'k')
%End switch statement for deciding on color of graph
end
%End for loop for different spontaneous emission factors
end
%Next graph will start anew.
hold off;
Current
(A)');
xlabel('Injection
ylabel('Power out (Watts)');
title('Power vs. Injection Current');
%Start a seperate graph
figure
plot(Xaxis,Yaxis2,'k')
title('Carriers vs. Injection Current');
figure
plot(Xaxis,Rst,'k')
title('stim. emission rates vs. current');
figure
plot(Xaxis,Rsp,'k')
title('spont. emission rates vs. current');
figure
plot(Xaxis,netgain,'k')
title('net gain vs. current');
unction SteadyState=Rate(N,I)
global V;
global Cauger;
90
global B;
global Asurf;
global Vp;
global Gamma;
global vg;
global go;
global Ntr;
global Bsp;
global alpha;
global Gamma m;
global alpham;
SteadyState=real(I/(1.6e- 19*V)-C_auger*N^3-Vp/V*Gamma*B*N^2-A_surf*NVp/V*Gamma*vg*go*log(N/Ntr)*Gamma*Bsp*B*N^2/(vg*(alpha+Gamma-m*
alpham-Gamma*go*log(N/Ntr))));
91
Bibliography
[1]
D. Miller, Dense opticalInterconnectionsfor silicon electronics, in "Trends in Optics," Academic
Press, New York (1992).
[2]
D. Miller, Opticsfor low-energy communication inside digitalprocessors:quantum detectors,
sources, and modulators as efficient impedance converters. Optics Letters 14, 146 (1989).
[3]
J.D. Joannopoulos, R.D. Meade, and J.N. Winn, Photonic Crystals, Princeton, New York (1995).
[4]
S.Y. Lin, et al, A three-dimensionalphotonic crystal operating at infared wavelengths. Nature
394, 251 (1998).
[5]
E. Yablonovich, Photonic band-gapstructures. J. Opt. Soc. Am. B. 10, 283 (1993).
[6]
J.I. Pankove, OpticalProcesses in Semiconductors, Dover Publications, New York (1971).
[7]
L.A. Coldren, S.W. Corzine, Diode Lasers and Photonic IntegratedCircuits. John Wiley and
Sons, New York (1995).
[8]
B. Zhao, A. Yariv, Quantum Well Semiconductor Lasers, in SemiconductorLasers, ed. E. Kapon,
Ch. 1, Academic Press, San Diego (1999).
[9]
H. Yokoyama, K. Nishi, T. Anan, Y. Nambu, S.D. Brorson, E.P. Ippen, M. Suzuki, Controlling
spontaneous emission and threshold-lesslaser oscillation with optical microcavities. Optical and
Quantum Electronics 24, S245 (1992).
[10]
Y. Yamamoto, S. Machida, G. Bjork, Micro-cavity semiconductor lasers with controlled
spontaneous emission. Optical and Quantum Electronics 24 S215(1992).
[11]
Y. Yamamoto, S. Machida, G. Bjork, Microcavity semiconductor laser with enhanced
spontaneous emission. Physical Review A. 44, 657 (1991).
[12]
D.C. Kilper, P.A. Roos, J.L. Carlsten, K.L. Lear, Squeezed light generatedby a microcavity laser.
Physical Review A. 55, R3323 (1997).
[13]
R.J. Ram, "Microcavity Lasers: Coherent Matter and Light," Ph.D. Thesis, Electrical and
Computer Engineering, University of California, Santa Barbara (1997).
[14]
E.V. Goldstein, P. Meystre, Spontaneous Emission in Optical Cavities: A Tutorial Review, in
Spontaneous Emission and Laser Oscillation in Microcavities,ed. H. Yokoyama, K. Ujihara, Ch.
1, CRC Press, Boca Raton, (1995).
[15]
Peter W. Milloni, The Quantum Vaccum. Academic Press, INC. San Diego, CA, (1994).
[16]
David J. Griffiths, Introduction to electrodynamics.PrenticeHall. Upper Saddle River, New
Jersey, (1999).
[17]
G. Bjork, S. Machida, Y. Yamamoto, K. Igeta, Modification ofspontaneous emission rate in
planar dielectric microcavity structure. Physical Review A. 44, 669 (1991).
92
[18]
J.M. Gerard, B. Sermage, B. Gayral, B. Legrand, E. Costard, V. Thiery-Mieg, Enhanced
spontaneous emission by quantum boxes in a monolithic microcavity, Physical Review Letters. 81,
1110 (1998).
[19]
E.M. Purcell, Spontaneous emissionprobabilitiesat radiofrequencies,Phys. Rev. 69, 681 (1946).
[20]
J.M. Gerard, B. Gayral, InAs quantum dots: artificialatoms for solid-statecavity-quantum
electrodynamics.Physica E. 9, 131 (2001).
[21]
H. Benisty, J-M Gerard, R. Houdre, J. Rarity (eds.), Confinedphoton systems. Springer. Berlin,
Heidelberg, (1999).
[22]
G.M. Yang, M.H. Macdougal, P.D. Dapkus, Ultralow thresholdcurrent vertical-cavity surfaceemitting lasers obtainedwith selective-odidation. Electronics Letters. 31, 886 (1995).
[23]
D.L. Huffaker, L.A. Graham, H. Deng, D.G. Deppe, Sub-40pA Continuous-Wave Lasing in an
Oxidized Vertial-CavitySurface-EmittingLaser with DielectricMirrors.IEEE Photonics
Technology Letters. 8, 974 (1996).
[24]
H. Altug, D. Englund and J. Vuckovic, Ultrafastphotoniccrystal nanocavity laser.Nature Physics
2, 484 (2006).
[25]
H. Park, S. Kim, S. Kwon, Y. Ju, J. Yang, J. Baek, S. Kim, Y. Lee, Electrically driven single-cell
photonic crystal laser. Science 305, 1444 (2004).
[26]
W.D. Zhou, J. Sabarinathan, P. Bhattacharya, B. Kochman, E.W. Berg, P. Yu, S.W. Pang,
Characteristicsof a photonic bandgap single defect microcavity electroluminescentdevice. IEEE
J. Quant. Elec. 37, 1153 (2001).
[27]
T.D. Happ, M. Kamp, A. Forchel, J. Gentner, L. Goldstein, Two-dimensionalphotonic crystal
coupled-defect laser diode. App. Phys. Lett. 82, 4 (2003).
[28]
R.J. Deri, E. Kapon, Low-Loss III-V Semiconductor Optical Waveguides. IEEE Journal of
Quantum Electronics. 27, 626 (1991).
[29]
H.Y. Liu et al. Improvedperformance of 1.3pm multilayerInAs quantum-dot lasers using a highgrowth-temperatureGaAs spacer layer. Applied Physics Letters. 85, 704 (2004).
[30]
A. Markina, "Design and Simulation for the Fabrication of Integrated Semiconductor Optical
Logic Gates," Ph.D. Thesis, Department of Electrical Engineering and Computer Science, MIT
(2005).
[31]
loffe-Physico-Technical Institute. (2003). PhysicalPropertiesof Semiconductors. Retrieved Dec.
18, 2006from New Semiconductor MaterialArchive:
http://www.ioffe.rssi.ru/SVA/NSM/Semicond/index.html
[32]
S.L. Chuang, Physics of OptoelectronicDevices, John Wiley and Sons, New York (1995).
[33]
Rajeev Ram, 6.731 Lecture Notes: Semiconductor Optoelectronics, Theory and Design (2006)
[34]
G. Bjork, A. Karlsson, Y. Yamamoto, Definition of a laserthreshold. Physical Review A. 50,
1675 (1994).
93
[35]
T. Baba, T. Hamano, F. Koyama, K. Iga, Spontaneous emissionfactorof a microcavity DBR
surface-emitting laser. IEEE Journal of Quantum Electronics. 27 1347 (1991).
[36]
K. Petermann, Calculatedspontaneous emissionfactorfor double-heterostructureinjection lasers
with gain-inducedwaveguiding.IEEE Journalof Quantum Electronics, 15, 566 (1979).
[37]
J. Vuckovic, 0. Painter, Y. Xu, A. Yariv, A. Scherer, Finite-differencetime-domain calculation of
the spontaneous emission couplingfactor in optical microcavities. IEEE Journal of Quantum
Electronics. 35, 1168 (1999).
[38]
R.J. Ram, D.I. Babic, R.A. York, J.E. Bowers, Spontaneous emission in microcavitieswith
distributedmirrors.IEEE Journal of Quantum Electronics. 31, 399 (1995).
[39]
R.J. Ram, E. Goobar, M.G. Peters, L.A. Coldren, J.E. Bowers, Spontaneous emissionfactor in
post microcavity lasers. IEEE Photonics Technology Letters. 8, 599 (1996).
[40]
A. A. Erchak, "Enhanced Performance of Optical Sources in III-V Materials Using Photonic
Crystals," Ph.D. Thesis, Department of Materials Science and Engineering, MIT (2002).
[41]
G. Bjork, Y. Yamamoto, Analysis of semiconductor microcavity lasers using rate equations. IEEE
Journal of Quantum Electronics. 27, 2386 (1991).
[42]
G. Bjork, A. Karlsson, Y. Yamamoto, Definition of a laser threshold. Physical Review A. 50,
1675 (1994).
[43]
E. Mattson, "Design and Fabrication of an Electrically-Activated Photonic Crystal Nanocavity
Laser," S.M. Thesis, Department of Electrical Engineering and Computer Science, MIT (2005).
[44]
J.A. Del Alamo, 6.742 lecture notes: Microelectronic Devices, an Integrated Approach. (2005).
[45]
T.C. Shen, G.B. Gao, H. Morkoc, Recent developments in ohmic contactsfor Ill-V compound
semiconductors. J. Vac. Sci. Technol. B. 10, 2113 (1992).
[46]
J. Thiery, H. Fawaz, A. Leroy, G. Salmer, Extremely low resistanceAu/Mn/Ni/Au ohmic contact
to p-GaAs. J. Vac. Sci. Technol. B. 13(5), 2130 (1995).
[47]
[48]
J.K. Abrokwah, J.H. Huang, J. Baker, T. Polito, W. Ooms, NiZnAl-Basedp-Type Ohmic Contacts
on AlGaAs/InGaAs Heterostructures.IEEE Transactions on Electron Devices. 40, 1185(1993).
T. Sanada, 0. Wada, Ohmic Contacts to p-GaAs with Au/Zn/Au Structure. Japanese Journal of
Applied Physics. 18, L491 (1980).
[49]
A.R. Clawson, Guide to references on
lHl-V semiconductorchemical etching. Materials Science
and Engineering. 31, 1 (2000).
[50]
K-Y Lim, "Design and Fabrication of One-dimensional and Two-dimensional Photonic Bandgap
Devices," Ph.D. Thesis, Department of Electrical Engineering and Computer Science, MIT
(1999).
[51]
J.A. del Alamo, T. Mizutani, AuGeNi ohmic contacts to n-InPfor FET applications.Solid-state
Electronics. 31, 1635(1988).
94
[52]
V.G. Weizer, N.S. Fatemi, Simple, extremely low resistancecontact to n-InP that does not exhibit
metal-semiconductorintermixing during sintering.Appl. Phys. Lett. 62, 2731 (1993).
[53]
R.J. Shul et al., New plasma chemistriesfordry etching ofInGaAlP alloys: B13 and BBr3. J. Vac.
Sci. Technol. B 16, 2690(1998).
[54]
S. Agarwala et al, High-density inductively coupledplasma etching of GaAs/AlGaAs in
BCl3/C12/Ar: A study using a mixture design experiment. J. Vac. Sci. Technol. B 16 511
(1998).
[55]
F. Ren, S.J. Pearton, J.R. Lothian, C.R. Abernathy, W.S. Hobson, Reduction ofsidewall roughness
during dry etching of SiO2. J. Vac. Sci. Technol. B. 10, 2407 (1992).
[56]
R. Lothian, F. Ren, S.J. Pearton, Mask erosion during dry etching of deepfeatures in III-V
semiconductorstructures. Semicond. Sci. Technol. 7, 1199 (1992).
[57]
Discussion with Professor Leslie Kolodziejski
[58]
J.A. Kong, Electromagnetic Wave Theory, BMW (2000).
[59]
Y. Xu, W. Liang, A. Yariv, J.G. Fleming, S-Y Lin, High quality-factorBragg onion resonators
with omnidirectionalreflector cladding.Optics Letters. 28, 2144 (2003).
[60]
P.L. Gourley, Biocavity laserforhigh- speed cell and tumour biology, J. Phys. D: Appl. Phys. 36,
R228 (2003).
[61]
E. Istrate, E.H. Sargent, Measurement of the phase shift upon reflectionfrom photonic crystals.
Applied Physics Letters. 86, 151112 (2005).
95